Interesting Math Theory Question

[mrxpibb]

Can zero and infinite be considered separate ideas, or related?

In addition, could they be the exact same thing?

[Darksage]

what do you mean 'separate ideas'?

[mrxpibb]

Are they different? I avoided the word 'things' because they obviously are not tangible.

[Darksage]

well zero is a number and an integer, infinity is neither, so they're not the same.

[mrxpibb]

well zero is a number and an integer, infinity is neither, so they're not the same.

Those are classifying groups, and a credible argument.

But besides how we classify them, what's the difference between the two?

[Darksage]

Just think about how any two numbers are different. They're different if:

They have different absolute values.
They have different additive and multiplicative inverses.
They have different factors.
Their quotient is not 1.
Their product is not the square of either.
Their sum is not double of either.
etc


Zero and infinity pass all of those conditions (each condition implies the other, so it's all or none):

|0| = 0, |∞| = ∞.
The additive inverse of 0 is 0. The additive inverse of ∞ is -∞. 0 has no multiplicative inverse. ∞ has no multiplicative inverse (or, it's 1/∞, not sure, but inconsequential).
0 has an infinite number of factors; itself and any other real number. ∞ only has one factor, itself.
0/∞ and ∞/0 are not 1.
0*∞ is indeterminate, but 02=0 and ∞2=∞
0 + ∞ = ∞, 2*0=0.

[mrxpibb]

But who's to say that infinite isn't zero? Isn't infinite the absence of nothingness?

[Darksage]

Just think about how any two numbers are different. They're different if:

They have different absolute values.
They have different additive and multiplicative inverses.
They have different factors.
Their quotient is not 1.
Their product is not the square of either.
Their sum is not double of either.
etc


Zero and infinity pass all of those conditions (each condition implies the other, so it's all or none):

|0| = 0, |∞| = ∞.
The additive inverse of 0 is 0. The additive inverse of ∞ is -∞. 0 has no multiplicative inverse. ∞ has no multiplicative inverse (or, it's 1/∞, not sure, but inconsequential).
0 has an infinite number of factors; itself and any other real number. ∞ only has one factor, itself.
0/∞ and ∞/0 are not 1.
0*∞ is indeterminate, but 02=0 and ∞2=∞
0 + ∞ = ∞, 2*0=0.

This is a proof that infinity and zero are not equal. If infinity is the absence of nothing, and zero is nothing, how would they be the same?

[mrxpibb]

This is a proof that infinity and zero are not equal. If infinity is the absence of nothing, and zero is nothing, how would they be the same?

Zero is absence of anything.

Once again, are they separate, interlinked, or the same?

[Darksage]

They are definitely not 'the same', as demonstrated in my above post. I don't know what you mean by "interlinked" or "separate". You can't describe these things in plain words after you've been presented with a rigorous, mathematical analysis.

[mrxpibb]

They are definitely not 'the same', as demonstrated in my above post. I don't know what you mean by "interlinked" or "separate". You can't describe these things in plain words after you've been presented with a rigorous, mathematical analysis.

1/0=infinite
1/infinite=0

Are they inverses, then?

[Darksage]

1/0 is not infinity, it's undefined. You can't divide by zero.Even if it were, your post doesn't show they're inverses. Multiplicative inverses multiply together to give you 1. 5 * 1/5 = 1, so 5 and 1/5 are inverses. Inverses are unique.

Ex for multiplication:
The inverse of 5 is 1/5
The inverse of 10/2 = 2/10

1/5 = 2/10
The inverses are equal

Therefore, the original numbers were equal.


You can't do that with infinity and zero, therefore they're not equal.

[mrxpibb]

You can't divide by either, and if you multiply you get either zero or infinite, depending on which one used.

So what makes zero a number? Because we call it that? It seems to have its own rules.

[kastoob]

This is inconceivable. 0 =/= infinity.

infinity + 1 = infinity
0 + 1 = 1

^ Ideas not related.

[mrxpibb]

This is inconceivable. 0 =/= infinity.

infinity + 1 = infinity
0 + 1 = 1

^ Ideas not related.

Infinite by itself is inconceivable. Zero is also inconceivable. We always think of something. If we see nothing we think of a vacuum.


How about absolute values? Those aren't related at all by your definition.

-2 + 1 = 1
2 + 1 = 3

[Darksage]

Infinite by itself is inconceivable. Zero is also inconceivable. We always think of something. If we see nothing we think of a vacuum.


How about absolute values? Those aren't related at all by your definition.

-2 + 1 = 1
2 + 1 = 3
Zero isn't inconceivable, and neither is infinity. That they are equal is what's inconceivable.

How about absolute values? Those aren't related at all by your definition.

-2 + 1 = 1
2 + 1 = 3

All I said about absolute values was:
Just think about how any two numbers are different. They're different if:

They have different absolute values.

I did not say that if two numbers have the same absolute value, they are equal, because that is false. All I said was if two numbers have different absolute values, they are guaranteed not to be equal.

All your example demonstrated is that -2 does not equal 2. If two numbers, x and y, are equal, then if you add any number z to both of them, their sums, x + z and y + z, should be equal. Thats why in kastoob's post:
This is inconceivable. 0 =/= infinity.

infinity + 1 = infinity
0 + 1 = 1

^ Ideas not related.

Demonstrated that infinity and zero are not equal. Infinity=x, 0=y, 1=z.

x + z = infinity + 1 = infinity
y + z = 0 + 1 = 1

Their sums are not equal, therefore, 0 and infinity are not equal.

[mrxpibb]

Zero isn't inconceivable, and neither is infinity. That they are equal is what's inconceivable.



All I said about absolute values was:
[/LIST]
I did not say that if two numbers have the same absolute value, they are equal, because that is false. All I said was if two numbers have different absolute values, they are guaranteed not to be equal.

All your example demonstrated is that -2 does not equal 2. If two numbers, x and y, are equal, then if you add any number z to both of them, their sums, x + z and y + z, should be equal. Thats why in kastoob's post:


Demonstrated that infinity and zero are not equal. Infinity=x, 0=y, 1=z.

x + z = infinity + 1 = infinity
y + z = 0 + 1 = 1

Their sums are not equal, therefore, 0 and infinity are not equal.

I only quoted Kastoob because that's all I was contesting. And he said they weren't related. So, if sums prove they aren't related, how do you explain absolute values? That's all I was saying.

[Jun-Kun]

I would like to think of an infinitely large conical surface in both directions (like the Light-Cone), where 0 is in the middle and infinity and minus infinity are at the ends.

[Sithreis]

You can't divide by either, and if you multiply you get either zero or infinite, depending on which one used.

So what makes zero a number? Because we call it that? It seems to have its own rules.

Because it's the value of nothing. And it's between -1 and 1 (lol) (and also the absolute midpoint between all positive and negative values.

It's the number of limbo!

(http://en.wikipedia.org/wiki/0_(number) lol that's a pretty long article)

[mrxpibb]

Because it's the value of nothing. And it's between -1 and 1 (lol) (and also the absolute midpoint between all positive and negative values.

It's the number of limbo!

(http://en.wikipedia.org/wiki/0_(number (http://en.wikipedia.org/wiki/0_%28number)) lol that's a pretty long article)

It's long because it needs to be. What is the value of nothingness?