Possible Math Breakthrough

[Lemniscate]

Inf to the power of a number > or = to 0 equals inf.

Inf to the power of a number < or = to 0 equals 0.

Inf to the power of 0 equals undefined.

 

Based on that, if inf is taken to the 0 power, it would be both inf and 0.

You may want to fix that to make sense.

[Dark]

@ Crab: I need to think more logically before I say something.

 

What I meant to say was that I consider the multiplication of numbers -1 < x < 1 as division, but that's wrong because of irrational numbers.

 

@ Lem: Probably a typo on my part, as the = signs should not have been there.

[Raylen]

@ Leminscate:

 

n^0 = 1. Anything ^0 = 1. You're multiplying inf by it self 0 times, which is just 1.

 

If that isn't proof enough, then this should be:

 

Keep in mind that x^y = x[x^(y-1)]. So x^(y-1) = x^y / x.

 

So inf^1 = inf (Dark's exponent Theorem), so inf^(1-1) = inf / inf

 

which gets us: inf^0 = 1.

[Dark]

@ Leminscate:

 

n^0 = 1. Anything ^0 = 1. You're multiplying inf by it self 0 times' date=' which is just 1.

 

If that isn't proof enough, then this should be:

 

Keep in mind that x^y = x[x^(y-1)']. So x^(y-1) = x^y / x.

 

So inf^1 = inf (Dark's exponent Theorem), so inf^(1-1) = inf / inf

 

which gets us: inf^0 = 1.

 

I don't believe that works with 0^0.

[Raylen]

That comes back to the original problem, what is 0/0 in this system?

 

Because looking back at our proof. If y = 0, then what?

 

You have 0 = 1/0, then 0 * 0 = 1, and 0 does not equal 1, so the proof falls apart.

[Dark]

Since we are dealing with infinity, I assume we can amend the concept that 0/0 equals undefined, as that is the real numbers.

 

Let's assume y = 0/0.

 

0 apparently equals x/inf.

 

(x/inf) / (x/inf)

 

(x/inf) x (inf/x)

 

infx/infx

 

That must equal 1.

 

So it'd be most logical for 0/0 to equal 1 in this scenario.

[CrabHelmet]

That must equal 1.

 

Even if we ignore the poor definitions and whatnot that plague this whole thing, this step still has no justification.

[Dark]

infx/infx

 

inf/inf equals 1.

 

So it'd be reduced down to x/x.

 

That would normally equal 1, unless x = 0. If x = 0, then I become heavily confused.

 

Because I was trying to figure out what 0/0 is in the first place. :/

[CrabHelmet]

inf/inf equals 1.

 

Again, why?

[Dark]

inf/inf equals 1.

 

Again' date=' why?

[/quote']

 

Theoretically, if you have an infinite amount of objects to give to an infinite amount of people, simple logic says that each person will get 1.

 

Mathematically, any nonzero number divided by itself equals 1.

 

2/2 = 1

569/569 = 1

.621/.621 = 1

 

Therefore, inf/inf = 1.

 

0/0 would equal 1, but it also equals 0 and undef. at the same time, giving it three answers when it should only have one.

[CrabHelmet]

inf/inf equals 1.

 

Again' date=' why?

[/quote']

 

Theoretically, if you have an infinite amount of objects to give to an infinite amount of people, simple logic says that each person will get 1.

 

Mathematically, any nonzero number divided by itself equals 1.

 

2/2 = 1

569/569 = 1

.621/.621 = 1

 

Therefore, inf/inf = 1.

 

0/0 would equal 1, but it also equals 0 and undef. at the same time, giving it three answers when it should only have one.

 

It depends on how you define your infinities, and poor definitions are going to be an insurmountable obstacle here. Remember, we have said INF*INF=INF, so if INF/INF=1, then 1=INF/INF=INF*INF/INF=INF*1=INF. Therefore, 1=INF. Absurd? Yes. But that's what you get when you attempt to imply complex binary functions to non-complex objects without proper definitions.

[Dark]

... :/

 

I can't really put a definition on infinity, can I?

 

Never should have involved myself in this. NEVER FEEL AMBITIOUS, GUISE!

[Raylen]

I'm still trying to help you Dark.

 

The best I could come up with was treat infinity as a variable.

 

For example, now we can have:

 

inf / inf = 1.

inf - inf = 0.

inf + inf = 2 inf

inf x inf = inf ^2

 

Where inf + x cannot be simplified. With the standard form of inf being a + b(inf)

 

So we can perform basic addition and subtraction:

 

For example: 3+5inf + 2 - 4 inf = 5+ inf.

[Dark]

Division and subtraction are just common sense. It's the rest of them that I wanted to make math out of. Just settling for undefined and using a + bi (when you replace i with inf.) is the easy solution and doesn't really amount to much.

[Raylen]

Well, I didn't say it was as much. But there are no contradictions this way.

[Dark]

That's true.

 

I'll sleep a night on this, and see what I can muster up.

 

But I highly doubt infinity has any real-world applications anyways... so this is just a waste of our time.

[BehindTheMask]

Dark. Then what is

 

0 divided by 0?

 

L'Hopitals Rule.

[Womi]

1/inf = 0.inf

 

"0.inf"? That's just nonsense.

 

Wrong.

[Scatty]

You have 2 of flaws.

 

First, inf minus inf is a tri-result equation, being at the same time -inf, 0, and inf.

 

Second, division by 0 is not impossible, as nothing is impossible in math. Let me explain:

 

 

In theoretic math, when 0 is used for a division, it is treated as 0.(0)1, or the closest number to 0, just as one third of 100 is 33.(3) So:

 

a / 0 = a / (0.(0)1/1) = a*100...0, where 0 repeats an infinity of times.

 

If a is higher than 0, the result is infinity. If a is lower than 0, the result is minus infinity. If a is 0, the result is 1 because you get a/a.

That's true.

 

I'll sleep a night on this' date=' and see what I can muster up.

 

But I highly doubt infinity has any real-world applications anyways... so this is just a waste of our time.

[/quote']

 

Everything is a waste of time.

[Raylen]

Use x, not . for multiplication. Or use a bullet. I see what you mean, but other people won't.

[Scatty]

that . wasn't for multiplication, it was a decimal dot.

 

As in pi is 3.14

 

When I used multiplication (look above), I used *.

 

And just because other people won't believe it, it doesn't mean it's not true. I always thought 0/0=1. Always.

[CrabHelmet]

1/inf = 0.inf

 

"0.inf"? That's just nonsense.

 

Wrong.

 

In that case' date=' would you care to explain exactly what you're jabbering about?

 

You have 2 of flaws.

 

First, inf minus inf is a tri-result equation, being at the same time -inf, 0, and inf.

 

Nonsense. There are more than three valid results. INF-INF could be any integer just as well as it could be zero.

 

Second' date=' division by 0 is not impossible, as nothing is impossible in math. Let me explain:

 

 

In theoretic math, when 0 is used for a division, it is treated as 0.(0)1, or the closest number to 0, just as one third of 100 is 33.(3) So:

 

a / 0 = a / (0.(0)1/1) = a*100...0, where 0 repeats an infinity of times.

 

If a is higher than 0, the result is infinity. If a is lower than 0, the result is minus infinity. If a is 0, the result is 1 because you get a/a.

[/quote']

 

This looks like some horrible, horrible corruption of the concept of Limits. Oh, and it's also just plain not true.

[Raylen]

Versatility, we've proved that already:

 

Let y = 1 / 0

 

We are given by Dark's last axiom' date=' 0 = 1/inf.

 

So, y = 1 / (1/inf)

 

This can be rewritten as

 

y = 1 / (inf^-1) [Dark's negative exponent axiom']

 

y = (inf ^ -1) ^ -1

 

y = inf ^ (-1 x -1)

 

y = inf ^ 1

 

y = inf [Dark's infinite exponent axiom]

 

So, therefore, 1/0 = inf.

 

However, what is 0/0? Is my question, this proof no longer works for 0.

 

However, the question was, if y=0. Then you have 0*0 = 1, which is obviously false.

[Zexaeon]

THE LAWS OF THE UNIVERSE ARE NOTHING.

 

Only THE VOID is infinite.

 

 

...

 

 

 

Okay, with that said, I like what you've done here. Clearly, several kinks had to be worked out from Page 1, due to the 3 subsequent pages of discussion, but it's kind of fun to establish rules for something Math Teachers never really teach you much about.

 

But I have one question...

 

Does Infπ equal..... infinite Pies? 8D *Shot*

[Muluck]

Wouldn't infinity just be a place holder, and not an actual number?

The reason why you never see a rule about infinity is because it isn't an actual number.

 

Using Algebra for my example here, take set-builder notation.

Now the way you would write an infinite amount in set-builder notation would be like this:

For the sake of time, I'll use inf for infinity.

{x|x > inf}

 

Now, when you go to graph that, the graph wouldn't stop a a certain number because you can never stop at one number and claim it to be the last of all numbers. Mathematicians developed the term Infinity or Infinite as a way to get around the fact that you cannot possibly count and store the highest number possible.

So instead they use a place holder, and because it is a place holder and not an actual number you cannot Add it, Subtract, Multiply it or Divide it by itself or any other number for that matter.

 

Note: The word Infinity or Infinite is typically used in graphing. Very rarely do you ever see it in an algebraic formula.

Also, I am not a Mathematician and certainly do not claim to be the best there is at this subject. It's just food for thought.