Integers is the set of numbers that includes “0”, negative and positive numbers ( …”-3″, “-2”, “-1”, “0”, “1”, “2”, “3”…). Integers are commonly accepted at face value and for the average person we don’t give them much thought, but recently I was thinking about them and after much deliberation I declare there is no such thing as a negative number.
In fact, negative numbers exist only as representations of the act of subtraction. Integers as a set is handy for symbolic representation of the act of subtraction for if you have 2 Ioaves of bread and subtract 2 you have 0 loaves of bread. Neat. We could present this problem as such:
2 – 2 = 0
Now, we see the set of Integers at work. Or do we?
I posit that we are only witnessing the symbol “-” (minus symbol) at work and not an entirely new number. 2 is 2 is 2. Since the set of Natural numbers does not contain “0” it does not suffice to satisfy when you have “0” loaves of bread, so in that Integers work well. But I think negative Integers need not be in the set of Integers to express what has already been declared subtraction. At this point we have simply expressed an infinite lateral mirror of numbers that are being infinity subtracted by, well, nothing.
Is your head being twisted up yet? I hope so because mine is.
I’m in a math club that has been officially dubbed the Social Mathematics Experiment or “S.M.E.” and it has sparked lots of interesting internal mathematical turmoil (thanks Professor Havens!). For instance, another little tidbit that has my mathematical underwear in a bunch is this:
If the Universe is infinitely expanding in all directions, then it is expanding into something. Well, what is that “something”? What is the Universe expanding into and if the Universe is infinitely expanding than that other “something” is infinitely decreasing. How can something infinitely decrease? Is this where negative Integers come into play? Because if it is then by that theory the expanding Universe is mirrored in all direction as a negative of itself, like the number line of Integers is ( …”-3″, “-2”, “-1”, “0”, “1”, “2”, “3”…) where we see that the infinite decrease is only a mirror of the Natural numbers but with a mathematical actor applied to them (subtraction, or “-“).
This tells me that there are at least 2 of everything. It seems since our Universe is infinitely expanding in all directions it would need infinite amounts of “mirrored” places to expand into that are the converse of this particular Universe that I write from right this instant. Which humors me because by the logic of negative integers there is a separate me typing this message negatively precisely the same distance negatively from where our 2 Universe’s meet from where I am. Since I am in prison, I am in prison in every Universe, infinitely, and that sucks. The good news is this, when I get out of prison I also get out infinitely. Yay!
Now, since I see the world this way I believe that the set “Integers” is fraudulent and misleading because it takes my mind captive and suggests that you can have -2 somethings, when you cannot, -2 is not an actual number but a mathematical equation, it is a math problem on its own merit and thus the set of negative Integers is simply an infinite amount of math problems.