Possible Math Breakthrough

[Raylen]

Anyways, Dark, what you need to do is create a mathematical system. There are rules that apply to this mathematical system, they are called axioms. We also need proper definitions so that the axioms can be applied. From the axioms we can derive theorems. But we need a proper definition first. The best I could come up with was a+b(inf), so I'll leave that to you...

[Dark]

And what if you want to multiply (1+6inf)(3+2inf)?

 

3 + 20inf + 12inf^2

 

Well, at least you can simplify down i^2 and make it -1. We can't really simplify inf^2, so it's just going to be the imaginary formula put into polynomial context.

[Womi]

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?

[/quote']

 

Well, I can try to express it in English.

We're talking about our normal decimal system, if I got that right.

So we are calculating with the base 10 to the power of any real number.

Expecting infinity is an infinite number going towards a nonexistent end of the decimal system, can't we also let it go towards the nonexistent end behind the point?

And isn't 2^inf = inf? Infinite is infinite, isn't it?

 

And 6*3 = 20? Orly?

[Raylen]

I have no idea. From now on if you want to write anything, please use LaTeX.

 

http://www.codecogs.com/components/equationeditor/equationeditor.php

 

Because I have no clue what anyone is talking about.

[Scatty]

Versatility' date=' we've proved that already:

 

Let y = 1 / 0

 

We are given by Dark's last axiom, 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.

 

I did not state 0*0=1, I clearly stated that 0/0=1, which is clearly true.

[Womi]

n/n=1 ; n € N

-> 0 € N -> 0/0=1

[Raylen]

I did not state 0*0=1' date=' I clearly stated that 0/0=1, which is clearly true.

[/quote']

 

Jesus,

Let's assign a value to , say it is y.

 

 

 

We see that y can be ANY value, not just 1. Yes 0/0 = 1, but it can be anything. So it has no defined value, therefore undefined.

[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?

[/quote']

 

Well, I can try to express it in English.

 

That seems reasonable.

 

We're talking about our normal decimal system' date=' if I got that right.

[/quote']

 

I see no reason not to do so, so certainly, let us stick with Base 10.

 

So we are calculating with the base 10 to the power of any real number.

 

what

 

The decimal system does not work that way. Scientific notation does not work that way. Common logarithms might work that way' date=' depending on what your wording means, but I can't see what they have to do with anything.

 

Expecting infinity is an infinite number going towards a nonexistent end of the decimal system, can't we also let it go towards the nonexistent end behind the point?

 

This also makes no sense whatsoever.

 

And isn't 2^inf = inf? Infinite is infinite' date=' isn't it?

[/quote']

 

Actually, depending on how you define infinity, that is provably false. Consider the number of natural numbers {1, 2, 3, ...}. There are an infinite number of natural numbers, and we name this particular infinite quantity "aleph-0". Now, raising 2 to the power of this cardinality - which is defined as counting the number of subsets of the natural numbers - produces another infinite quantity. However, this new infinite quantity is provably not equal to "aleph-0" but rather is strictly greater; we call it "aleph-1".

 

And 6*3 = 20? Orly?

 

You don't even know how to multiply binomials properly. Based on this, I believe I can safely say that your nonsensical ramblings are indeed pure nonsense and not merely my failure to understand your insightful genius.

[Dark]

(1+6inf)(3+2inf)

 

And 6*3 = 20? Orly?

 

Basic binomial multiplication? FOIL? Front, outer, inner, last?

 

I learned that easily in sixth grade.

[Womi]

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?

[/quote']

 

Well, I can try to express it in English.

 

That seems reasonable.

 

We're talking about our normal decimal system' date=' if I got that right.

[/quote']

 

I see no reason not to do so, so certainly, let us stick with Base 10.

 

So we are calculating with the base 10 to the power of any real number.

 

what

 

The decimal system does not work that way. Scientific notation does not work that way. Common logarithms might work that way' date=' depending on what your wording means, but I can't see what they have to do with anything.

 

Expecting infinity is an infinite number going towards a nonexistent end of the decimal system, can't we also let it go towards the nonexistent end behind the point?

 

This also makes no sense whatsoever.

 

And isn't 2^inf = inf? Infinite is infinite' date=' isn't it?

[/quote']

 

Actually, depending on how you define infinity, that is provably false. Consider the number of natural numbers {1, 2, 3, ...}. There are an infinite number of natural numbers, and we name this particular infinite quantity "aleph-0". Now, raising 2 to the power of this cardinality - which is defined as counting the number of subsets of the natural numbers - produces another infinite quantity. However, this new infinite quantity is provably not equal to "aleph-0" but rather is strictly greater; we call it "aleph-1".

 

And 6*3 = 20? Orly?

 

You don't even know how to multiply binomials properly. Based on this' date=' I believe I can safely say that your nonsensical ramblings are indeed pure nonsense and not merely my failure to understand your insightful genius.

[/quote']

 

YOUR INTELLIGENCE ALSO SURPRISING ME

[Scatty]

I did not state 0*0=1' date=' I clearly stated that 0/0=1, which is clearly true.

[/quote']

 

Jesus,

Let's assign a value to , say it is y.

 

 

 

We see that y can be ANY value, not just 1. Yes 0/0 = 1, but it can be anything. So it has no defined value, therefore undefined.

 

Math does not work that way. You cannot assign the value y=0/0 just to say afterwards that y=anything. In what you said, you have just proven that y=anything, not that 0/0=anything.

 

 

 

Let me repeat what you said:

 

say y=3

 

y*0=3*0

 

Now, using your logic, it would seem that y here can be anything, so...3 can be anything?

[Mehmani]

Technically, the Speed of Light is Infinity because can ever travel faster than it according to Einstein's Theory of Relavitity (except maybe the building blocks of matter 1/10000000000000000000000000000th of a second after the Big Bang).

[Scatty]

Technically' date=' the Speed of Light is Infinity because can ever travel faster than it according to Einstein's Theory of Relavitity (except maybe the building blocks of matter 1/10000000000000000000000000000th of a second after the Big Bang).

[/quote']

 

We are not talking speeds here, we are talking numbers, or "weightless quantities", as they are named, that can be of any value.

[Raylen]

 

Math does not work that way. You cannot assign the value y=0/0 just to say afterwards that y=anything. In what you said' date=' you have just proven that y=anything, not that 0/0=anything.

 

Let me repeat what you said:

 

say y=3

 

y*0=3*0

 

Now, using your logic, it would seem that y here can be anything, so...3 can be anything?

[/quote']

 

*Facedesk*

 

I said some value, y (because we don't know) is equal to 0/0. Using logic, I proved y = anything, if and only if it equaled to 0=0, therefore there is no answer = 0.

[CrabHelmet]

Technically' date=' the Speed of Light is Infinity because can ever travel faster than it according to Einstein's Theory of Relavitity (except maybe the building blocks of matter 1/10000000000000000000000000000th of a second after the Big Bang).

[/quote']

 

No, the speed of light is a finite quantity, and you are horribly misunderstanding relativity - unless, of course, you mean that its speed is infinite from its own perspective, but I don't think anyone has ever chatted with a photon regarding its observations. The amount of energy needed to accelerate an object of positive finite mass to the speed of light is transfinite, though.

[Womi]

 

Math does not work that way. You cannot assign the value y=0/0 just to say afterwards that y=anything. In what you said' date=' you have just proven that y=anything, not that 0/0=anything.

 

Let me repeat what you said:

 

say y=3

 

[b']y*0=3*0

[/b]

Now, using your logic, it would seem that y here can be anything, so...3 can be anything?

 

*Facedesk*

 

I said some value, y (because we don't know) is equal to 0/0. Using logic, I proved y = anything, if and only if it equaled to 0=0, therefore there is no answer = 0.

 

To solve this, you have to divide by zero.

[Raylen]

Anything times 0 is 0. So you just multiply by 0 on both sides, 0 x (0/0) = 0, and y*0 = 0. No dividing by zero is neccessary.

[WTF]

Anything times 0 is 0. So you just multiply by 0 on both sides' date=' 0 x (0/0) = 0, and y*0 = 0. No dividing by zero is neccessary.

[/quote']

 

true. but did dark say anything about variables and algebraic problems?