# Concept of Quantity

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• 03-17-2011
User Name:
Quote:

Originally Posted by C_ntua
So to clarify one more time, 0.999... cannot be proven to be equal to 1
a) Without axioms about infinite sums
b) Without axioms about decimals with infinite digits
c) Without something else

AND if this is attempted the definition of infinity will save 90% of arguing, so people can give their definition of infinity at least in the sense of "infinite decimal digits"

b implies a, so you could shorten your list, if you want.

In general, aren't all decimal expansions infinite sums? Decimal representation - Wikipedia, the free encyclopedia

What makes equations that involve infinity wrong?
• 03-31-2011
KAUFMANN
Any number multiplied by its inverse is 1 since N*(1/N)=1 because the N's cancel on each other. Now, since 0 is the inverse of infinity, is it safe so assume that 0*infinity=1? Methinks so.
• 03-31-2011
whiteflags
0 isn't the reciprocal of infinity.

inf/inf = 1
1/inf = 0
0inf = 0

All of these are made rigorous by the limit concept.
• 03-31-2011
brewbuck
Quote:

Originally Posted by whiteflags
0 isn't the reciprocal of infinity.

inf/inf = 1
1/inf = 0
0inf = 0

All of these are made rigorous by the limit concept.

They are rigorous if you actually write them as limits. Written in the above way they are just nonsense.
• 04-01-2011
GReaper
Think of it this way:
Think infinity as the universe ( and ignore my signature :D ).
The universe is constantly expanding. Likewise, two infinities may not be the same...

I know... I think... I guess... who am I kidding? :D
• 04-01-2011
Mario F.
Quote:

Originally Posted by KAUFMANN
Any number multiplied by its inverse is 1 since N*(1/N)=1

Except 0. Otherwise...

0 * (1/0) = 1

Quote:

because the N's cancel on each other. Now, since 0 is the inverse of infinity, is it safe so assume that 0*infinity=1? Methinks so.
Since the above shows you, I hope, that 0 can't be the inverse of infinity (infinity has no inverse), 0 * infinity must be constructed differently. The current agreement is that infinity multiplied by any number, including 0 is undefined.
• 04-01-2011
User Name:
Quote:

Originally Posted by KAUFMANN
Any number multiplied by its inverse is 1 since N*(1/N)=1 because the N's cancel on each other. Now, since 0 is the inverse of infinity, is it safe so assume that 0*infinity=1? Methinks so.

It depends. Do you mean 0 multiplied by something that approaches infinity or something that approaches 0 multiplied by something that approaches infinity? If the former, no, it would be 0. If the latter, sometimes; It could approach anything, because it is an indeterminate form(Indeterminate form - Wikipedia, the free encyclopedia).

Quote:

Originally Posted by whiteflags
inf/inf = 1
1/inf = 0
0inf = 0

lim(x->inf)x/lim(x->inf)x^2 = lim(x->inf)x/x^2 = lim(x->inf)1/x = 0
The second is correct. (I even used it above.)
lim(x->inf)1/x * lim(x->inf)x = lim(x->inf)x/x = lim(x->inf)1 = 1

The first and third are indeterminate, and can't be given a general rule.
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