## Negative numbers don't exist proof inside

### #16

Posted 20 September 2008 - 06:29 AM

### #17

Posted 20 September 2008 - 06:47 AM

Math has nothing to do with natural law.

Math is a system that man devised to measure and predict the environment. Everything in math comes from logic. We define things that we would like to have, define operations, and then figure out all the possible implications.

There is no nature in this logic. There is only man in this logic. Every implication taken from math can be taught to be absolutely true.

The assumptions, however, which are our base definitions and operations, may not be.

Since I cannot even determine that 1+1=2 without defining natural numbers, the addition operation, equivalence, cardinal order, etc., there is no way I can say that 1+1=2 is once and absolutely true for all circumstances. I can only say that given that these assumptions and operations are true, this is definitely true.

There are other systems of logic, within math, that define 1+1=2 to be non-true, because they deal with different assumptions. Likewise, 0 doesn't exist in many maths, but "negligible" does.

Just a small thought exercise illustrating why zero isn't always a useful part of math.

Can I ever say there are 0 people in a room? If I am in the doorway of a room, would we say that there are 1/2 people in the room? Or 1? If 1, than we could say that there is 1 person in the other room of the doorway, as well. Now we can add up the number of people in each room to discover that there is 1 more person in the house than there actually is.

Now, if I can say half a person, what if I have my foot in a room, and the rest of me outside the window? 1/20th of a person?

Now, what if I leave dead skin cells all over the place, but am otherwise not in the room? 1/5000000th of a person? 0 people? Negligible people?

It isn't always useful to use the number 0, it just almost always is, which is why algebra accepted it after 250 years of argument. Sometimes, it's useful to use negligible as well as 0, in the same calculations, sometimes, it's impossible to use zero, such as when everything is relative.

Humans will never understand the universe. We will simply get better and better at predicting it. The only way to perfectly understand a universe is to create it . . . and I can mathematically prove that! (you just have to accept my assumptions)

### #18

Posted 20 September 2008 - 10:26 AM

When trying to decide how many people are in a room, first you have to define "in" (if I'm in the doorway, am I in the room? If someone permanently changed the room, can it be said that they are still "in" the room because we can feel their effects?), then you have to define the people, (are dead skin cells people? Is a foot people?), and then you might as well define room (maybe the doorway is part of the room? Wait, am I talking about a particular instance of time or maybe how many people have ever been in the room?). Once you have all those silly definitions and notation out of the way, you can calculate how many people are in the room, if you really want to. No one is saying that calculation would be useful.

You don't believe 1+1=2? Fine, maybe you're working in a system where the only numbers are 1 and 0, so 1+1=0. Maybe you believe 1+1=3, which is demonstrably false unless you're in a coherent system that allows that. But you can't just make stuff up because it's easy or useful.

### #19

Posted 20 September 2008 - 12:12 PM

You don't believe 1+1=2? Fine, maybe you're working in a system where the only numbers are 1 and 0, so 1+1=0. Maybe you believe 1+1=3, which is demonstrably false unless you're in a coherent system that allows that. But you can't just make stuff up because it's easy or useful.

Actually, making up stuff because it's easy or useful is something we do, all the time, in science.

It is the essence of science.

Thus why, for basic fluid mechanics, we deal with "dry water". A fluid that has none of the properties of a fluid, but can be used to predict, roughly, how real fluid acts.

Thus why we imagine elementary particles as spheres.

Thus why we say that a water molecule has 1.5 bonding strength.

In mathematics, it is the essence of mathematics. All of math was made up, literately made up of nothing, because it was useful, first, then generalized, and then to make it easy we removed as many contradictions as possible.

As a pure mathematics student, I come across systems that disagree with algebra all the time. In set theory, number theory, ring theory, calculus, etc.

Care for an example?

### #21

Posted 20 September 2008 - 12:56 PM

-The League Against Tedium

### #22

Posted 20 September 2008 - 01:01 PM

### #23

Posted 20 September 2008 - 01:17 PM

There are 10 kinds of people in the world. those that understand binary and those that don't.

But anyhow, that's just switching the base.

I'm talking about logic that depends on different assumptions and therefore has drastically different system of arithmetic.

Such as, for example, the proof that the zeros of quantum-level organized formulas will always be prime, (Called quantum-organized because it was a math invented for predicting quanta interactions, by a doctor of physics). The proof requires that one accepts a set of numbers outside of the normal algebraic form that contain only numbers that have certain factors. Those factors are actually undefined, but we can create finite subspaces in that numberline which contain only numbers that have certain defined factors, (but we find quickly that we can't define them how we want to and still get a useful result), and then prove that we can extend those subspaces to infinity, and then prove that every of these numbers will produce a non-zero result. This means that we can prove that the zeros will always be prime, but not that every prime will produce a zero on any given QO formula.

On that numberline, the numbers are completely different. For example, if we add the first number in that series to itself, we receive the 5th number in the series. Weirdly enough, if we add the 4th number in the series to itself, we get the 2nd number in the series.

Because the numberline provably gets bigger, and because we don't actually need to add these numbers at any point, we take the easy way, and say that addition is undefined for them.

An interesting usage of these numbers means that we can prove that .9 repeating need not equal 1. The case is actually ambiguous depending on your interpretation of i. However, if we accept that i is outside of the normal numberline, (the usual assumption), than .9 repeating is actually equal to 1.

This post has been edited by **FFreak3**: 20 September 2008 - 01:30 PM

### #26

Posted 20 September 2008 - 01:49 PM

I know a very small amount amount binary: ie what it is, what constitutes a bit and a byte, and how binary works in analogue to digital (and vice versa) conversion.

-The League Against Tedium

### #29

Posted 21 September 2008 - 12:02 AM

### #30

Posted 21 September 2008 - 06:56 AM

But yes, everything else IS up for doubt. Let's drop a heavy ball. What guarantees are there that it will drop to the ground? Well, experience and gravity. Between those two you can

*nearly*guarantee that the ball will drop. But some circumstances may cause otherwise. Gravity may act as a repelling force, (never seen before, but it still seems possible that could happen, particularly given superstring theory), gravity could weaken, causing the ball to fall away into a very low orbit, (until it crashes into an anthill), some force we haven't yet observed could manifest, some force we have observed but not understood yet could manifest . . . etc. etc.

One of the hopes of the LHC, for example, is that we will be able to understand gravity better, in which case, the hope, (not of the scientists, they roll their eyes at this), is that we will be able to use that knowledge to make anti-gravity vehicles, (The engine to harness the anti-gravity, even if gravity can be used like that, would probably be larger than a helicopter, and probably much louder).

@slade: Sometimes nature is a complex and obtuse object, and then you need complex math to match that you can use to predict it. Hopefully you can break down the problems enough that you can use simpler math as much as possible, but that isn't always possible.

I noted that this series of numbers was made to prove that all zeros of any quantum-organized forumla, a physics formula, would always be prime. Nature is a beast down there, and we unfortunetely constantly need extremely complex math to analyse those situations. Particularly since the calculations for approximations would take years to make.