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Sudden Demand For Logicians On Wall Street 525

An anonymous reader writes "In an unexpected development for the depressed market for mathematical logicians, Wall Street has begun quietly and aggressively recruiting proof theorists and recursion theorists for their expertise in applying ordinal notations and ordinal collapsing functions to high-frequency algorithmic trading. Ordinal notations, which specify sequences of ordinal numbers of ever increasing complexity, are being used by elite trading operations to parameterize families of trading strategies of breathtaking sophistication. The monetary advantage of the current strategy is rapidly exhausted after a lifetime of approximately four seconds — an eternity for a machine, but barely enough time for a human to begin to comprehend what happened. The algorithm then switches to another trading strategy of higher ordinal rank, and uses this for a few seconds on one or more electronic exchanges, and so on, while opponent algorithms attempt the same maneuvers, risking billions of dollars in the process."
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Sudden Demand For Logicians On Wall Street

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  • And the moral is: (Score:5, Insightful)

    by Mathinker ( 909784 ) on Thursday May 27, 2010 @01:50AM (#32358350) Journal

    Buy gold.

    (Half in sarcasm, since if the world economy collapses totally, it would probably be better to have something like, say, food.)

  • by serps ( 517783 ) on Thursday May 27, 2010 @01:51AM (#32358352) Homepage

    How long can this trend be maintained before major problems arise in the economy ?

    before problems arise? Have you not been paying attention for the last two years?

  • by feepness ( 543479 ) on Thursday May 27, 2010 @01:52AM (#32358356) Homepage

    Well, at the expense of whom?

    Currently, other traders with less sophisticated algorithms.

    How long can this trend be maintained before major problems arise in the economy ?

    Until they start gets jobs as Secretary of the Treasury and writing laws that distort markets in their favor at the expense of everyone.

  • by Z34107 ( 925136 ) on Thursday May 27, 2010 @01:54AM (#32358368)

    But everything thus far shows us that perpetual growth is possible. Technology is a wonderful thing - each year we're able to do more with less.

    That's not to say that a lot of what goes on in the market isn't pure, unadulterated bullshit, but real, honest-to-goodness "growth" won't stop until technology does.

  • by pyalot ( 1197273 ) on Thursday May 27, 2010 @01:55AM (#32358378)
    What you seem to fail to realize is that growth has nothing to do with making a profit in derivative markets. And high frequency algorithmic trading has been here before, and now they step up that game. So as far as "change" goes, nothing has really changed, and nothing will, high frequency algorithmic trading is here to stay. If anything, this is making markets much more volatile. And if you think last weeks 1000 DOW drop was an exception, those are going to be more frequent.
  • by ls671 ( 1122017 ) * on Thursday May 27, 2010 @02:04AM (#32358410) Homepage

    > Technology is a wonderful thing - each year we're able to do more with less.

    A perpetually growing economy usually involves the average wage rising so average people can buy more stuff while still working less.

    Have you looked around lately ? In fact you are right in some way: every year we need less people, so by the market rule, the average wage goes down relatively to what you can buy for a dollar on average, especially food and lodging.

  • by pushing-robot ( 1037830 ) on Thursday May 27, 2010 @02:05AM (#32358416)

    perpetual growth is impossible to achieve in a finite universe.

    Technically, you only need to improve until everyone is happy. In other words, when we invent Soma. Or holosuites.

    Whether that's reassuring or terrifying is left as an exercise to the reader.

  • by Anonymous Coward on Thursday May 27, 2010 @02:10AM (#32358454)

    That's one of the stupidest comments I've ever heard on here. No, really. It is.

    Long term investment is the POINT of a stock market. It's to encourage the private sector to ALLOCATE MONEY EFFICIENTLY toward PRODUCTIVE activity. Shuffling money around constantly and making the only "productive" part the cut you get for the shuffling (not the actual thing you invested in) completely defeats that purpose. It's called RENT SEEKING by the banks and traders, and it's a BAD THING. It encourages money to be allocated poorly in a short sited fashion, only doing whatever will make the most commission for the trader and his company. It does the opposite of what the stock market was supposed to do.

    Great googly moogly have people become so blinded by day trading as to think making money on the trading was the point of the market? If that's the way you're thinking, then just withdraw your life's savings from the bank, drive your ass to Las Vegas, and start "investing". You can be well ahead of Wall Street's curve on what they're trying to sustain: a massive legalized national casino.

  • by sqrt(2) ( 786011 ) on Thursday May 27, 2010 @02:19AM (#32358508) Journal

    There will always be people who will not be satisfied with our current level of understanding, the current state of technology, and the current prospects for humanity's future. As has been true for all time, these people will push civilization forward.

  • by mwvdlee ( 775178 ) on Thursday May 27, 2010 @02:23AM (#32358522) Homepage

    Some people are mentally defective and will only be happy when they have more than others. Two such persons and they'll keep fighting eachother until everybody loses.

  • by Anonymous Coward on Thursday May 27, 2010 @02:24AM (#32358524)

    every year we need less people, so by the market rule, the average wage goes down relatively to what you can buy for a dollar on average

    In this small minded view, the poster assumes partially correctly that the law of supply and demand works with intellectual capital.

    If less and less people are required to do _everything_, I guess this may hold true. However, in an ever expanding economy, the "stuff" that needs to be done expands faster than the ability of people to do it, even when aided by technology.

    So far, this has been true as far back as I can read in any history book (including wikipedia)

    Technological advancement will not outpace our ability for production as a law of nature. The people on this planet that are capable of making the great leaps forward in common thinking are so few, that there has been no sign of technology getting ahead of our ability to use it to it's fullest. Several "Giant Leaps" would need to happen before this thought process could be proven to hold water.

    IMHO - and I'm the worlds authority on that. ;)

  • by HishamMuhammad ( 553916 ) on Thursday May 27, 2010 @02:27AM (#32358546) Homepage Journal

    Those of us in the rest of the world, who have been suffering being the weaker part in the worldwide marketplace game, we've been paying attention for much longer than two years.

  • by sqrt(2) ( 786011 ) on Thursday May 27, 2010 @02:27AM (#32358550) Journal

    This is one of the best comments I've read about this issue.

    Too many people see things exactly as you describe. The "market" is just an abstraction, they don't make the connection to the real world companies that they are investing in because they don't see that as the point anymore. It used to be that you could take a small amount of money, invest it in a company with a good idea - along with many other people - and you could profit from it too. Getting money to people with good ideas, and letting people who could never start their own company have a chance to be involved in the process of business, that was the goal. Now, Wall Street is about finding new ways to creatively move, funnel, transfer, shuffle, and convert money so that when it comes out of the other side of the black box it's more than you started with. It might as well be a casino, instead of a random number generator or dice you have the ups and downs of real companies creating the random seed.

    It would be funny if not for the fact that the rest of the US, the world really, are subsidizing this farce and allowing these people to get rich doing nothing productive.

  • by Anonymous Coward on Thursday May 27, 2010 @02:34AM (#32358584)
    Technically, you only need to improve until everyone is happy.

    Actually, you only need to kill people until the survivors stop complaining.
  • by Rick Bentley ( 988595 ) on Thursday May 27, 2010 @02:35AM (#32358594) Homepage
    This will end poorly (again). It's basically a bunch of business majors managing a poorly understood programming effort, but instead of running things in a development environment they're running it on massive computers and the variables are REAL MONEY. Hiring mathematicians to write their algorithms won't likely help, they will eventually do something stupid, divide by 0, have unbounded growth, or otherwise watch their program crash along with the market.

    I'm cashing out everything, buying canned food and ammo and moving to a farm.
  • by Anonymous Coward on Thursday May 27, 2010 @02:37AM (#32358600)

    The same banks that perform HFT also act as brokers. They know where everybody's stop losses are. They can run your stops and cause you to sell, while triggering other people to sell the market short, then run the market back up and cause the shorts to cover, and cause you to buy again so you don't miss out. Rinse and repeat.

  • by Jah-Wren Ryel ( 80510 ) on Thursday May 27, 2010 @02:47AM (#32358656)

    this system rewards people who produce nothing of value, make nothing, enrich no one's lives, do not create art, do not expand the sphere of human knowledge, and provide no meaningful service to humanity or the country.

    If only it were so simple. Efficient allocation of capital is extremely useful. It enables all kinds of progressive development that would never occur otherwise and stock markets (and derivative markets) are the best way humanity has come up with to do it. You might as well be arguing that farmers' markets and cattle auctions are just as useless - all they do is provide a meeting place and a means to buy and sell - they create nothing.

    It should come as no surprise that the system can and is abused - that's pretty much the case for every system man has ever come up with. But to argue that capital markets are nothing more than siphons from the poor to the rich is to throw the baby out with the bath water.

  • by Jah-Wren Ryel ( 80510 ) on Thursday May 27, 2010 @03:09AM (#32358818)

    Shuffling money around constantly and making the only "productive" part the cut you get for the shuffling (not the actual thing you invested in) completely defeats that purpose. It's called RENT SEEKING by the banks and traders, and it's a BAD THING.

    No, it's not. Arbitrage is a much closer definition to what's going on - they are trying to treat one big market as if it were a bunch of micro-markets (as the time between trades gets shorter it effectively breaks the market up based on ranges of trading speed) and are looking to profit on the difference between them. If they were actively trying to screw with the markets - like pulling a pump-and-dump scheme, or bribing politicians for favorable laws, that would be a form of rent-seeking. But millisecond gambles on minute fluctuations in price is not rent-seeking any more than year-long gambles on large fluctuations in price is rent-seeking.

    It encourages money to be allocated poorly in a short sited fashion, only doing whatever will make the most commission for the trader and his company. It does the opposite of what the stock market was supposed to do.

    You are confused here. Sure there are people who think they can be individual players doing high-frequency trades and there are brokers willing to accommodate them. But they are a drop in the sea. The real money moving around is coming from funds, mostly the kind that are only available to high net-worth people. Those fund managers aren't trying to maximize brokerage fees, they charge a management fee regardless of the number of trades. Sure they may manipulate the system to max out any performance-based bonuses, but that's a common problem with any sort of fund, not just the ones that do high-frequency trading.

  • by SpaceLifeForm ( 228190 ) on Thursday May 27, 2010 @03:17AM (#32358858)

    Have you not been paying attention the last 40 years?

    This is all about having an excuse for their machinations.

    They will blame the geeks in court.

  • by ppanon ( 16583 ) on Thursday May 27, 2010 @03:45AM (#32359014) Homepage Journal

    Efficient allocation of capital is extremely useful. It enables all kinds of progressive development that would never occur otherwise and stock markets (and derivative markets) are the best way humanity has come up with to do it.

    Stock markets for efficient allocation of capital, sure. Derivative markets, that's questionable, and in some cases downright laughable.

  • by Ultracrepidarian ( 576183 ) on Thursday May 27, 2010 @03:45AM (#32359020)
    The trickle has taken on a decidedly yellow tinge.
  • by Anonymous Coward on Thursday May 27, 2010 @03:57AM (#32359082)

    It's not necessarily a bad thing, if you realize this, then you can easily predict a stock's movement and make some easy income; knowing exactly where the low and high values are going to be at any point in time. Again, the only thing that causes a stock to change its movement is actual human interaction that results in the trend being broken.

    So we should just leave it to the computers and sit back, getting rich while not producing anything?
    That does sound like a bad thing, and it's pretty much what got us into the mess we're in.

  • by AK Marc ( 707885 ) on Thursday May 27, 2010 @04:14AM (#32359144)
    I hesitate to say the entire stock market in general because at its core there is something useful

    The "fix" is to have trades once every minute, and no more than that. Trades are executed to the number of "requests" times 90% (if there are 100 sell requests and 200 by requests, the lowest number of 100 is taken, multiply by .9 and so there will be 90 trades that minute). The sell and buy orders are randomly selected and then processed. Those passed over will be at the top of the queue for the next minute. I'm sure it would take some serious refining, but the idea is to completely eliminate microsecond fluctuations, eliminate priority trades, and make it "fair" for all. Either that, or make the market completely open where anyone can log on from anywhere and do a trade as if they are a broker. That would introduce many more problems than just batches and delays with limited processing, but it would fix many of the problems we have now.

    But, anyway it goes, there needs to be a complete re-write of the stock market. It's been perverted from the paper trading to a good-ol-boys network of computers with systemic abuses aimed at hurting people trying to use the system in good faith. As it sits now, abolishing the stock market and having companies sell their own stock in paper in person at their corporate headquarters would be a massive improvement. Sadly.
  • by Jah-Wren Ryel ( 80510 ) on Thursday May 27, 2010 @04:44AM (#32359252)

    Do you honestly believe there were no systemic abuses when it was all paper? That just seems so incredibly naive.

  • by RajivSLK ( 398494 ) on Thursday May 27, 2010 @04:48AM (#32359258)

    then you can easily predict a stock's movement and make some easy income;

    If it's that easy why aren't you a billionare? (or are you?)

  • by Tom ( 822 ) on Thursday May 27, 2010 @04:49AM (#32359264) Homepage Journal

    It's a fundamental flaw.

    The incentive to do the right thing (long term investment into production) is - money. If there is another way to make the same money easier or faster, or make more money or even make more money easier and a lot faster, then a rational participant in the market will do it.

    Now, the stock market is a closed system - any buck that the day trader made, someone else had to put in. The stock exchange doesn't generate any value. So if nothing else convinces you, then ask yourself where all these short-term pure trading profits come from. If you still haven't realized after all the bailouts: It's you.

    Can't really blame the traders. They ran a highly profitable scam for many years, then it all blew up. They probably couldn't believe their luck when the tax payer stepped up to cover all the losses and didn't even stop the scam. So heck yes do they continue, of course. Who wouldn't?

  • by Tom ( 822 ) on Thursday May 27, 2010 @04:51AM (#32359270) Homepage Journal

    So they figured that by using "high-frequency algorithmic trading" they could keep the profits coming in.

    "Profit" in the extended meaning of the word. There is no value being generated at the exchange, only well, duh - exchanged. So the value that they take out of the market ("profit") is something someone else had put in.

    Well, at the expense of whom ? How long can this trend be maintained before major problems arise in the economy ?

    Welcome to our time traveller from 2005. You may want to read up on the news to find your answers there. The short version:
    a) everyone else
    b) about 4 years, which were over in 2009.

  • by TheLink ( 130905 ) on Thursday May 27, 2010 @04:59AM (#32359310) Journal

    It's also about marketing, bullshit and "plausible deniability".

    This is so the gamblers can give better excuses/bullshit for gambling with other people's money. This way everyone can say it's some sophisticated stuff that few people understand, so they get to keep their bonuses and profits when it all blows up.

    Here's an analogy: the financial system is a casino. The casino doesn't produce any "real" wealth - it just distributes it. The Federal Reserve produces the casino chips (trillions of them if necessary). The casino operators take their cuts+fees. The players gamble with OTHER people's money (pension funds etc), and when they win they get pay raises and bonuses. If a single gambler loses big, he loses his job. If a huge bunch of gamblers lose big, they say "bail us out". How can a huge bunch of gamblers lose at the same time? They can if they play a "let's create fake wealth" game.

    Here's a popular version: you start with a "parcel". You sell it for a profit to the next person. And the next person may do the same thing and so on. Whoever currently holding the parcel is allowed to declare that they are richer by the current "outside" value of the parcel. When the "music stops" the parcel is opened and the holder gets whatever is inside (which may be a bunch of IOUs).

    It doesn't really need very much sophistication to play such games.

    Here's another game: this is a trading/auction game: a few players pay the casino a special amount and they then get to see other people's bids 30 milliseconds[1] before everyone else does and they also get to make bids and cancel their bids rapidly. Naturally this is very profitable for those few players, unless there is a bug in their software, and they make a big loss in which case they ask the casino to rollback the trades, or change the rules so their losses are limited.

    This needs a bit more sophistication if you are aiming for maximum profit since your program has to "battle" the other programs. But the few with the 30 millisecond advantage should make money from the rest.

    Lastly, the gamblers who get sacked for losing will often get rehired since even if their companies lose big and maybe even go bankrupt, they make their _bosses_ rich.

    [1] []

    Simplified version of how it works: []

  • by purpledinoz ( 573045 ) on Thursday May 27, 2010 @05:08AM (#32359376)
    Isn't this some kind of insider trading? They are trading based on information before it is made public, but in the milliseconds range. The problem is the big players are given huge advantages, like free money from the Fed, while the rest of us suffer from the resulting inflation. Goldman Sachs and JP Morgan are way too powerful, they are powerful enough to destroy a currency, like the Euro.
  • Love it! (Score:3, Insightful)

    by jumpifzero ( 1815880 ) on Thursday May 27, 2010 @07:52AM (#32360224)
    Society is so fucked up that people are being paid 7 figure salaries to develop smarter gambling algorithms, that produce no real value, when they could help solving science hardest problems. Specially people with this knowledge.
  • by u38cg ( 607297 ) <> on Thursday May 27, 2010 @08:09AM (#32360352) Homepage
    The reason price fluctuates throughout the day is not internal to the company, but external. The price at any moment is fixed by supply and demand, and the demand for a particular stock is driven by any number of things: commodities prices, a presidential election in Brazil, long term weather forecasts, portfolio rebalancing, performance of a related stock, etc. All of these things take place within a network, where A affects B affects C affects D affects A.
  • sounds logical (Score:1, Insightful)

    by Anonymous Coward on Thursday May 27, 2010 @08:31AM (#32360518)

    sounds like a "man-in-the-middle" attack.
    the 10% of humans that own near everything in the world
    really need to wake up to the idea, that living in a fairytale
    castle in the middle of a vast slump is not as cool as
    living in a so-so mansion surrounded by green rolling hills
    with fresh vegetables and eggs everyday, non?
    anyways, if you want to invest, there only one thing to invest in: robotics and automation.
    unfortunately the big machine creator firm are all more or less privately own, since
    they are smart and don't want greedy short-term thinking "shareholders" interfering
    with their plans.

  • by Herkum01 ( 592704 ) on Thursday May 27, 2010 @08:49AM (#32360720)

    Why should they be delayed only a minute, why not a day? If they are a true stockholder, a day to wait is nothing. It is only people who are trying to skim money off transactions between people who are cannot wait. By comparison, stock owners hold most of the value in a company and we should be paying attention to their interests. Instead we have bent over and allowed faster traders to rule the roost against the best interests of everyone.

  • by AK Marc ( 707885 ) on Thursday May 27, 2010 @09:00AM (#32360836)
    You can't pervert something that is already perverted

    I don't believe you. It was a perverted paper system further perverted by the computerization. Perhaps you'd have preferred that I have "further" inserted there, but the lack of that word doesn't mean that the previous system wasn't perverted.

    something is either corrupt or it is not.

    It was corrupt before. The existing corrupt paper system was further perverted with the computerization.

    Hence you wrote that the paper system was not perverted.

    I wrote that the system was perverted by computerization. You inferred that to mean that I thought the paper system was perfect. You are wrong.

    If you want to argue about what I meant. I have explained it. If you want to argue about your opinion about what you think it could have meant when it's been demonstrated exactly what I did mean, then go fuck yourself.

    Perhaps YOU should read what's written, not what you were thinking when you wrote it.

    You are apparently arguing that it can be taken one and only one way, the way you assert. You are wrong. You have been further corrected with what I meant explained so there is no confusion in your little mind.

    And while you are at it, you might want to try adding a little bit of that civilized conversation too.

    I have no patience for those who always assume the worst when there's more than one way to take things. You are such a worthless pedant. So you get no such treatment when you have demonstrated yourself to be an uncivilized pedant who like to assume the worst possible interpretation and attack it. When you grow up and act like an adult, I might show you courtesy. But you've demonstrated you don't deserve any, so I'll not bother with the niceties.
  • by Fractal Dice ( 696349 ) on Thursday May 27, 2010 @09:49AM (#32361364) Journal

    4 seconds is too long to leave an opportunity of more efficient reallocation of capital unexploited, yet there are people who have been unemployed for over a year? This implies that we've created an economic system where it is a more efficient use of resources to rearranging ownership of theoretical constructs than finding a place in society for people who have none? Doesn't it seem that we've sort of lost sight of what the purpose of an economy is?

  • by Maxo-Texas ( 864189 ) on Thursday May 27, 2010 @09:54AM (#32361424)

    You should read on. Especially the cited material.

  • by DemApples ( 1770824 ) on Thursday May 27, 2010 @10:23AM (#32361768)
    I worked at one of the banks being lambasted here in a group that I left, within a year my peeps advised me that the group disappeared OVERNIGHT with no explanation. They pay big money to make the SEC an empty shell of what it's supposed to be doing (policing them). We need a big legal fence put up to keep these sharks away from "cash in a barrel" situations like being brokers and traders for the same products, and we need to vet any and all new products that hit the marketplace. Do we not remember the $4/gallon gas situation, an overnight doubling in price caused by pure speculation when we allowed oil companies to act as their own brokers? Wall Street banks bought oil companies and started Milken the public like crazy (pun unavoidable). Trusting Wall Street to not grab any and all cash it can any way it can is like trusting a starving 20 foot python to babysit your infant.
  • by Anonymous Coward on Thursday May 27, 2010 @11:28AM (#32362702)

    agreed, Love how people read only the material that best suits their agenda.

    FYI, you missed the part about how certain companies get access to seeing all the bids coming in a few milliseconds before they go through...

    Please tell me how that ends up helping the economy?

  • by oatworm ( 969674 ) on Thursday May 27, 2010 @12:39PM (#32363848) Homepage
    Oh, we can do better than that...

    Imagine you have a thing for classic cars and so do all your friends and coworkers. One of the coworkers says that he just bought a sweet classic car - maybe an early '60s Riviera or something - for cheap and wants to sell it at "fair market value". One of your buddies hears about the deal and says, "Yeah, I'll do that!", then buys the car. However, the buddy thinks that the amount he paid for the car is too low; after a bit of research, he decides that this particular car might be worth more than the coworker thought. So, he puts in the paper at what he thinks is fair market value, along with an explanation of why he thinks the value of this car is what he thinks it is. Lo and behold, another coworker looks at the description and buys the car. Then he, in turn, tries to sell the Riviera for a profit, telling anyone who will ask that this particular car has nearly doubled in value over the past year, so clearly there's money to be made.

    This continues for a while until suddenly the Riviera is out of buyers, at which point the last buyer of the car is effectively forced to do something that none of the other buyers have done - find out how the danged thing runs. If the last buyer is lucky, he'll have a sweet running Riviera on his hands and won't have to spend his life savings rebuilding it - this would be "creating wealth" (i.e. converting money to a productive car). If he's unlucky, he just got a Riviera with a rusted undercarriage, a fried transmission, and an engine with a cracked block - this would be "destroying wealth" (i.e. converting money to a non-productive lump of scrap iron).

    That's economics in a nutshell.
  • Not again?! (Score:3, Insightful)

    by crovira ( 10242 ) on Thursday May 27, 2010 @01:08PM (#32364310) Homepage

    Look for these very mechanisms to be banned by congress, the senate and possibly by presidential decree as the kind of "wealth creation without effort but strictly through gaming the system" which led us down the same path that derivatives did.

    All of the gains were wiped out and everybody but the insiders got stuck with the multi-trillion dollar tab when the music stopped and we found out the chairs were rented and had all be repossessed.

    These are the kinds of games which should be outlawed.

  • by Jah-Wren Ryel ( 80510 ) on Thursday May 27, 2010 @03:37PM (#32366940)

    Actually, it IS rent seeking. They do absolutely no productive thing and yet the money flows by virtue of them wedging themselves into the market. That's the very foundation of rent seeking.

    Except that they are adding value by increasing liquidity - they are acting like thousands of micro-market-makers with micro-spreads instead of the comparatively massive spread of traditional market makers.. Nor are they 'wedging' themselves anywhere, they have no more control over the market than any other participant.

  • by roman_mir ( 125474 ) on Friday May 28, 2010 @07:08AM (#32373812) Homepage Journal

    No, you are wrong and it's not funny because your ideas are the same that lead to economic collapse that is being observed currently.

    Reagan era 'deregulation' that just 'happened' to coincide with the fall of the USSR and beginning of globalization and movement of the jobs to cheaper places. Jobs are moved by Monopolies, show me one monopoly that does not rely on government(s) to become/continue being a monopoly.

    Government creates monopolies and destroys economy by creating them and pushing the idea of consumption over idea of production by artificially lowering interest rates on money, which they can do because they print money and give it to the preferred monopoly corporations in the first place.

    I VALUE PRODUCTION. Gold is a store of value when other currencies fail and governments are the reasons that currencies fail. Once the USD and other currencies are out, gold will be reused again, just like every time before to restart economy of production.

  • by minstrelmike ( 1602771 ) on Friday May 28, 2010 @10:33AM (#32376024)
    The problem with minimum wage laws is that they do not set the bottom wage, they merely remove possible wages below it.
    If I could work for dollar increments, then I can work for $1/hr or $2/hr or $3/hr and so on and so forth.
    When legislation demands a $7/hr minimum, then my options are this:
    $0, then $7/hr then $8/hr and so on.
    The bottom option of zero dollars never disappears, it just gets more common when min wage laws are enacted.

God made the integers; all else is the work of Man. -- Kronecker