Infinity

[Lullaby Chainer]

What are your views on infinity?
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Is there such a thing in the real world?
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Is our universe infinite?
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Is there such a thing in the math world?
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Can infinity be used in math?
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Can infinity be multiplied, divided, added, or subtracted in a math equation?
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If so, how would that be done?

[Slevin57]

Practically we have to assume infinite is a possibility. Certainly there is a limit to combinations of things, for instance replies to this topic but computing every possible reply would be near impossible, so were going to call it infinite replies.

[Renwood]

The second and third questions fold into one another for me; one definite example of infinity from my perspective and knowledge is the universe itself. Its time and size defeat us.

Quote by: Lullaby Chainer Can infinity be used in math?

Since you can always add or subtract one more from any number, the idea of infinity seems to me to be a certainty, and a necessity.

[ZNFYRH]

Quote by: Lullaby What are your views on infinity?

It's a lot.

Quote by: Lullaby Is there such a thing in the real world?

Being able to perceive infinity is contradictory to the definition of infinity, so while there might be, we'll never really know.

Quote by: Lullaby Is our universe infinite?

Unknown. Anyone who answers otherwise is just guessing. See the previous answer.

Quote by: Lullaby Is there such a thing in the math world?

Yes.

Quote by: Lullaby Can infinity be used in math?

Yes.

Quote by: Lullaby Can infinity be multiplied, divided, added, or subtracted in a math equation?

Yes.

Quote by: Lullaby If so, how would that be done?

By referencing the totality of infinity.

Infinity is a concept.

After reading the other thread on this topic from a few months ago I agree that when dealing with a concept you need to speak out what you are doing.

Division...

How many times does infinity go into infinity? Once.
∞ / ∞ = 1

How large is a segment if you divide something into an infinite number of segments? Not zero.

1 / ∞ != 0

(!= means "not equal to"... learned that in the other thread and =/= looks weird)

How many times does nothing go into nothing? Forever.

0 / 0 = ∞

[Yasa]

Quote by: ZNFYRH It'sHow many times does infinity go into infinity? Once. ∞ / ∞ = 1

wrong, INF/INF is undefined.

Quote by: ZNFYRH 1 / ∞ != 0

The limit is 0. Also, if you think of it like breaking an object apart. You are not done the equation untill you have done everything it says. For example, 10/2=5, end of operation. But if you attempt to divide something forever, you will never be done dividing, and will never obtain a the final pieces of whatever it was you were dividing. Personally, i believe x/INF to be a paradox and a series, not a number, but the limit is zero.

Quote by: ZNFYRH How many times does nothing go into nothing? Forever. 0 / 0 = ∞

Yet, based on your INF/INF logic, it should equal one. It is undefined because 0 could go in INF times, 0 times, or one times (or any amount of times for that matter).

[Yasa]

Quote by: ZNFYRH Infinity is a concept.

It is a concept, yet you said it can be used in mathematical operations too? What is 1/democracy?

infinity is good game and causes a lot of problems.

[Lullaby Chainer]

Quote by: ZNFYRH By referencing the totality of infinity.

Isn't "totality" contradicting to infinity?

Quote by: ZNFYRH How many times does infinity go into infinity? Once. ∞ / ∞ = 1

Infinity should have no limit as to what it can hold. Why not two infinities? Three?

Quote by: ZNFYRH How large is a segment if you divide something into an infinite number of segments? Not zero. 1 / ∞ != 0

How do you divide something an infinite number of times? If not zero, what is it? If you give ANY number other than zero, you'll be describing infinity as a FINITE number because you can now define INF by setting it to X and solving *example*. If you give zero, you'll be saying it's possible to make numbers or objects in the real world disappear entirely, denying the laws of physics (matter cannot be created or destroyed) by simply dividing it, which also goes against the definition of division.

*example* 1/∞=X [] ∞=1/X If x=any number other than zero, you've now found the exact number for infinity. That's crazy talk. *example*

Math says 100/∞ * ∞/100 = 1. Or at least it should.

∞/100 MUST be infinity. If you give ANY other number.. you can find the specific number of infinity by multiplying you answer by 100. This, of course, is absurd.

What times infinity is equal to 1?

ALL numbers times infinity equals infinity.

Thus the equation is absurd and infinity cannot be treated as a number.

Quote by: ZNFYRH (!= means "not equal to"... learned that in the other thread and =/= looks weird)

!= is classic C programming That's where it comes from.

Quote by: ZNFYRH How many times does nothing go into nothing? Forever. 0 / 0 = ∞

Infinity is equal to zero?

[Yasa]

Quote by: Lullaby Chainer Math says 100/∞ * ∞/100 = 1. Or at least it should.

It's undefined actually. We could write it as 100 * INF/INF * (1/100) and INF/INF is undefined.

Quote by: Lullaby Chainer Thus the equation is absurd and infinity cannot be treated as a number.

I agree.

[Lullaby Chainer]

Quote by: Yasa It's undefined actually. We could write it as 100 * INF/INF * (1/100) and INF/INF is undefined.

Makes sense.. except for the last part. INF/INF is undefined? Wouldn't it equal 1? Something divided by itself always equals one..


Also, another point brought up in another thread.

Is it even POSSIBLE for space and the real world to be infinite? I remember hearing some pretty good arguments against it in the other thread. (or maybe I'm just remembering my own arguments )

[Yasa]

Quote by: Lullaby Chainer Makes sense.. except for the last part. INF/INF is undefined? Wouldn't it equal 1? Something divided by itself always equals one.. Also, another point brought up in another thread. Is it even POSSIBLE for space and the real world to be infinite? I remember hearing some pretty good arguments against it in the other thread. (or maybe I'm just remembering my own arguments )

Nope, it's undefined because of the nature of itself. If you try and divide infinity infinitely you won't end up with an aswer.

As for your second question, my answer is yes and no. haha.

[ZNFYRH]

Lullaby,

How is it that splitting something finite can give you nothing?

That doesn't seem to make sense to me. By your logic, you're saying INF/INF would equal 0 as well.

1/INF does not equal zero. It's infinitely close, but the only way, in math, to start with something and to end up with nothing is with subtraction.

[Lullaby Chainer]

Quote by: ZNFYRH Lullaby, How is it that splitting something finite can give you nothing? That doesn't seem to make sense to me. By your logic, you're saying INF/INF would equal 0 as well.

No, I said.. IF you give a number other than zero.. [argument]

Then I said..

If you give zero, you'll be saying it's possible to make numbers or objects in the real world disappear entirely, denying the laws of physics (matter cannot be created or destroyed) by simply dividing it, which also goes against the definition of division.

[ZNFYRH]

So... then...

We're in agreement that X divided by infinity is NOT zero?

[5010]

According to Infinity (Wikipedia)

x/∞ = 0 (where x is a real number) but 0·∞ is indeterminate (except in some contexts). It also states that [x/∞ = 0] is not equivalent to [0·∞=x].

So is there an error in this wiki, or is there disagreement, or is it coming from a different context?

And could one say x/∞ = dx? The infinite slice is infinitessimal?

[ZNFYRH]

Let me put it simply...

How does something (a finite number) get turned into nothing?

No matter how many times you slice that finite something, it only makes smaller pieces of a finite something.

If 1 / INF = 0, then does 0 * INF = 1? That's just retarded.

The Wikipedia source even states that INF is not a real number. But if you allowed it to be part of an extended line then those formulas would be valid.

I think it's shift that they will definitively say that 1 / INF is 0, but will cry "undetermined" when you perform simple math and multiple both sides by INF.

[5010]

Perhaps some calculus finds it useful to define it that way. I don't know.

But as for whether or not one can experience infinity, I say it is possible. For example, my present existence is infinitely valuable to my future existence. There is nothing of greater value that can possibly be offered to me later in exchange for my life now, because there won't be a me to receive it!

[SoccerfreakAB2]

Quote by: 5010 According to Infinity (Wikipedia) x/∞ = 0 (where x is a real number) but 0·∞ is indeterminate (except in some contexts). It also states that [x/∞ = 0] is not equivalent to [0·∞=x]. So is there an error in this wiki, or is there disagreement, or is it coming from a different context? And could one say x/∞ = dx? The infinite slice is infinitessimal?

In my AP Calculus class, infinity is ONLY used as a limit, like as X approaches infinity. So infinity, for the most part, is never used in the question, nor the answer; it is a concept. It's the assumption that when the graph you're working with, or the equation, or the statistic, or whatever, is moved to an increasing amount of values for x, a pattern occurs.

This pattern could be that as X approaches infinity, your Y value could keep decreasing to 0, or could be increasing forever with your X.

Basically, in calculus at least, infinity is used to define continuities and patterns between equations and their graphs.

As for the value of x/∞, this is the same as 1/∞ times x. As I said before, 1/∞ is not a specific number, but a concept, where we can assume that 1 divided by an increasing sum of numbers will keep approaching 0 forever and ever; so essentially, in math at least, we write it down as 0.

I hope that helps some.

[ZNFYRH]

Approaching zero isn't the same as actually being equal to zero.

[SoccerfreakAB2]

Quote by: ZNFYRH Approaching zero isn't the same as actually being equal to zero.

What's your point? I'm saying that the value becomes so infinitely small that realistically we assume it becomes 0. Math is not philosophical, it's pragmatic.

[ZNFYRH]

I thought it was precise?