Infinity * Zero = Any Number ARGUE HERE

[GuidoHunter]

What my Cal IV professor told me to do was to just think of "really ****ing big" in place of infinity. It works for where I need it and explains the stick/stone thing nicely.

--Guido

http://andy.mikee385.com

[tsugomaru]

We've already argued this issue on so many levels.

Yes, for every stick, you can find a stone and for every stone, you can find a stick.

But if we were to place our hand down at any point of this pattern, we can say there'll be more stones than sticks.

~Tsugomaru

[GuidoHunter]

Originally Posted by tsugomaru

But if we were to place our hand down at any point of this pattern, we can say there'll be more stones than sticks.

~Tsugomaru

If you place your hand down, we cease to be considering infinity.

That's not how it works, Tsu.

--Guido

http://andy.mikee385.com

[DDRKirby]

Originally Posted by A2_Sauce

I've been very curious about this, please post comments.

Proof:

Any number / Infinity = Zero -- because anything divided by infinity will be infinitely small or zero.

Therefore Infinity * Zero = Infinity -- when you put infinity on the other side.

The first part stems from:

The limit as x->infinity as in the equation 1/x^2 will be zero, since x is approaching an infinately small number which would basically be zero.

However, if an variable were placed in the numerator....

the limit as x->infinity of the equation x/x^2 would be zero, and x^2/x would be undefined. However, it would be ridiculous to say infinity squared.

We could use a different variable to represent any number.

q=[0,00) {double zeros in this case is my lazy attempt at the infinity sign}

So, the limit as x->00 in q/x will be zero.



The second equation would be kinda strange:

Infinity * Zero = Infinity.

Since, if we were to solve for zero (treating it as a varable)....

Infinity/Infinity = 0.

Everyone knows that something divided by itself is 1, not zero.

However, I think it was a typo...

I think it should have been:

Any number / Infinity = Zero -- because anything divided by infinity will be infinitely small or zero.

Therefore Infinity * Zero = Infinity -- when you put infinity on the other side.

----

Infinity*zero = Any Number

Anything times zero is zero, not a mysterious unknown number.

I think I need more theortical Calculus....rofl.

[Kit-]

64/16 = 4/1 because the 6s cancel

[tsugomaru]

Originally Posted by GuidoHunter

If you place your hand down, we cease to be considering infinity.

That's not how it works, Tsu.

--Guido

http://andy.mikee385.com

Ahh man you are right. =[

~Tsugomaru

PS - Man, I was thinking about that when I was writing the statement.

[Kilgamayan]

Originally Posted by DDRKirby

The second equation would be kinda strange:

Infinity * Zero = Infinity.

Since, if we were to solve for zero (treating it as a varable)....

Infinity/Infinity = 0.

Everyone knows that something divided by itself is 1, not zero.

However, I think it was a typo...

I think it should have been:

Any number / Infinity = Zero -- because anything divided by infinity will be infinitely small or zero.

Therefore Infinity * Zero = Infinity -- when you put infinity on the other side.

----

Infinity*zero = Any Number

Anything times zero is zero, not a mysterious unknown number.

Any number divided by 1 is itself, and any number times zero is zero. Infinity is not a number, and the amount of people in this thread that still fail to grasp that concept stuns me.

Also, for the people whining about inf - inf, it is possible for it to equal zero, but it's not defined as zero. It's an indeterminacy, just like inf/inf, 0/0 and a whole bunch of other power crap. None of those things are defined to be anything - your goal when you run across one is to hit it with whatever you've got (L'Hopital's Rule is almost always a good place to start) to turn it into something that is explicitly defined.

[tsugomaru]

Kay, I need one more run through.

If inf-inf can equal 0, does that mean that it can also equal 1, 2, 3,...?

~Tsugomaru

[Kilgamayan]

It's possible, yes.

For example, take the size of the set of non-negative integers and subtract the size of the set of positive integers.

It's inf - inf, but the answer is 1.

[Kit-]

Originally Posted by Kilgamayan

It's possible, yes.

For example, take the size of the set of non-negative integers and subtract the size of the set of positive integers.

It's inf - inf, but the answer is 1.

Bijection:
0<->1
1<->2
2<->3

etc. etc.

[eagleboy]

Infinity * Zero is NOT any number, it's zero. No matter how large infinity is, any number you multiply by zero, is zero itself. You can have an infinite number of groups of zero, and it's still going to be zero, whatever way you put it. Still not satisfied? Think of it as a never-ending series of the numbers 0-9. Each of them times zero is zero, so therefore any VALUE, even INFINITY, must equal zero.

I would know, I aced Trigonometry AND Calculus (Not Pre-Calc) at age 15.

Infinity IS NOT a number, agreed. It's SO MASSIVE in amount that we dare not print it, because its value would exceed even the hardiest supercomputer's tolerance threshhold.

However, since infinity is never-ending, it's therefore a tangible value, just one that is too large to be properly expressed. We can argue all we want, but it remains a fact that, since infinity is never-ending, it must be an endless sequence of the ten basic digits, and, as these ten digits multiplied by zero are all zero, infinity * Zero MUST, by the transitive property, equal ZERO.

Here's the layout:

If 0*0=0, 0*1=0, 0*2=0, etc.
Then (Any single digit)*0=0.

If infinity is an endless string of digits
And (All digits)*0 equal zero
Then All of (Infinity*0)'s digits equal zero.
Therefore, by the transitive property, Infinity*0 = 0.

You just got served... math style. HOO-RAH!

[spyke252]

wrong eagle.

Infinity * k/infinity (Where k is a constant) can equal k.

Therefore, disproof-
Infinity * 6/infinity can equal 6 != 0.

[A2_Sauce]

Originally Posted by eagleboy

Infinity * Zero is NOT any number, it's zero. No matter how large infinity is, any number you multiply by zero, is zero itself. You can have an infinite number of groups of zero, and it's still going to be zero, whatever way you put it. Still not satisfied? Think of it as a never-ending series of the numbers 0-9. Each of them times zero is zero, so therefore any VALUE, even INFINITY, must equal zero.

I would know, I aced Trigonometry AND Calculus (Not Pre-Calc) at age 15.

Infinity IS NOT a number, agreed. It's SO MASSIVE in amount that we dare not print it, because its value would exceed even the hardiest supercomputer's tolerance threshhold.

However, since infinity is never-ending, it's therefore a tangible value, just one that is too large to be properly expressed. We can argue all we want, but it remains a fact that, since infinity is never-ending, it must be an endless sequence of the ten basic digits, and, as these ten digits multiplied by zero are all zero, infinity * Zero MUST, by the transitive property, equal ZERO.

Here's the layout:

If 0*0=0, 0*1=0, 0*2=0, etc.
Then (Any single digit)*0=0.

If infinity is an endless string of digits
And (All digits)*0 equal zero
Then All of (Infinity*0)'s digits equal zero.
Therefore, by the transitive property, Infinity*0 = 0.

You just got served... math style. HOO-RAH!

you are wrong eagle... any number * zero is zero... you are right on that one... but infinity is not a number... pretty much falsifying your whole arguement.

[itmorr]

0! isn't zero though

[eagleboy]

Originally Posted by spyke252

wrong eagle.

Infinity * k/infinity (Where k is a constant) can equal k.

Therefore, disproof-
Infinity * 6/infinity can equal 6 != 0.

Sorry, Spyke.

You're trying to disprove me by multiplying Infinity by a number other than zero. Therefore, your disproval attempt is moot.

A2, you're taking it out of proportion.

I SAID that infinity is not a number. You can't falsify my argument, though, because, you can have as many groups of zero items as you want, and you'll still have zero items overall.

I believe that this argument is mine. LOL

[talisman]

inf * 0 is undefined. It is not zero. It is not inf.

[Squeek]

multiplication: The operation that, for positive integers, consists of adding a number (the multiplicand) to itself a certain number of times. The operation is extended to other real numbers according to the rules governing the multiplicational properties of positive integers. --dictionary.com

Since infinity isn't a number, you can't even put it in the formula for multiplication.

In theory, no matter how many times you multiply something by zero, it's going to be zero. This is logic.

In math, when you try to multiply by something that isn't a number, you get "undefined" as the result.

You cannot multiply or divide infinity. It's not a number. I'll concede to allowing you to add numbers to infinity (as pointless as it will be and as illogical as it sounds to add numbers to something that isn't a number, like adding three to apple), but that's it.

Aperson's here, so I'll shut up now.

[aperson]

Originally Posted by Shashakiro

Oh, the weirdness of infinity. So many people don't understand it properly at all, because they try to think of it intuitively--and nothing about mathematical infinity is intuitive.

See, the reason 1^inf is undefined is beacause of these rules:

1^anything = 1
Anything^inf = inf

From a set theoretical standpoint, however, if the cardinality of the infinity with which you are raising the set of {1} to the inf is countable, then {1}^inf should be an evaluable operation, provable by recursive proof. If it has uncountable size, though, then the operation is undefined.

Originally Posted by Shashakiro

No matter how convinced you are that you're right here, you aren't. All of higher math disagrees with you.

Additionally...

If you were to show that the group of {1,^} is closed under the operation of ^ (i.e., it is not possible to generate an element outside of {1} no matter how many times 1 ^ 1 is performed), then it might be possible to argue that 1 ^ inf will equal 1 as well.

Calculus is not all of 'higher math', and believing so is prescribing to tunnel vision.

Originally Posted by itmorr

Why is infinite - infinite undefined?

Because not all infinities have the same size.

Originally Posted by Squeek

Worst of all is when professors are like "NO CALCULATORS. NO NOTES WITH FORMULAS."

That's totally realistic on real-world applications right there. When working, you'll never ever be able to look things up on the Internet. You'll have to pull it all from memory and do all the work on paper.

I'm in classes like 'Abstract Algebra' and 'Ring Theory' and everything is still no notes no calculator... There's a reason for this. Most of the formulas that you'll be dealing with are a) intuitive or b) derivable. It definitely shows a deeper understanding of math if you are able to reason out the formula or derive it from what you know. Just like right now, I don't remember all of the matrix operations and eigenvalue work to solve most linear algebra problems I'd run into, but I can reason them out based on the structure of matrices and solve one if I ran into it.

Originally Posted by GuidoHunter

What my Cal IV professor told me to do was to just think of "really ****ing big" in place of infinity. It works for where I need it and explains the stick/stone thing nicely.

--Guido

http://andy.mikee385.com

Yeah, for Calculus this is pretty much the best way to think of infinity because it covers the scope of it for limits very well. For other areas of math, like set theory though, very serious and rigorous notions of infinity are developed.

For example, there is the same cardinality of sticks and pebbles in the stick/pebble example. The set of all sticks and the set of all pebbles are both countably infinite sets. Through bijection, you can map each stick and each pebble to the set of Natural Numbers. Therefore, both sets have the cardinality (size) , which is the size of the Natural numbers. Sets of size are considered 'countably infinite.' Any set larger than this has the size of the Reals, and is uncountably infinite. (However, the question whether there are any sets larger than \aleph_0 and smaller than the reals is Undecidable.


Also, Squeek, as much as you axiomatize the system of grammar in the English language and hate derivations from it, I'd imagine you'd be quite a stickler for memorizing large pages of axiomatized formulaic waste. If you think you understand Calculus so well, take Real Analysis. After all, it should make all of those derivation and integration lists become intuitive.


Sadly, this thread is more of an argument of semantics than one of mathematics.

[eagleboy]

Originally Posted by talisman

inf * 0 is undefined. It is not zero. It is not inf.

Wrong, Talisman. It's simpler to think of it in the grade school way:

You know how 6 groups of 5 apples equal a total of 30 apples?

An infinite number of groups of 0 apples, means a total of 0 apples.

As for the k/infinity crap? Unless k is zero, technically, k/infinity is unequal to zero. It may be infinitely small, but even that means it's something.

Proof of Infinity * 0 = 0:

If infinity is the concept of all possible numbers, and all possible numbers times 0 equal zero, so would infinity, as all of its number set retains the same quality. So in summation:

Infinity is the concept of all possible numbers. (True)
All possible numbers end up zero when multiplied by zero. (True)
Thus, by the transitive property, Infinity equals zero when multiplied by zero.
(True by the laws of logic.)

Any more questions?

[aperson]

Infinity is the concept of all possible numbers. (True)


This assumption is not true therefore your argument is fallacious.