1) Infinity*zero= ??
2) Infinity 1= ??(I was thinking that, if it is one less than infinity then is it truly infinity??? )
Infinity*zero= ??
Re: Infinity*zero= ??
I think no.(1) will be 0 and no.(2) will be infinity

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 Joined: Wed Jan 21, 2015 11:14 am
Re: Infinity*zero= ??
The answer of question no.(1) will be 0 and question no.(2) will be infinity
Re: Infinity*zero= ??
I don't think Infinity is a number... it is a concept...
 Fm Jakaria
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 Joined: Thu Feb 28, 2013 11:49 pm
Re: Infinity*zero= ??
Actually ''en.wikipedia.org/wiki/Cardinal_number'' may help you understand arithmetic's of infinity. Generally you can 'classify' sets to be 'equivalent' if they posseses a bijection. In this notion; 'infinity' is not a single element; there are variations of infinity[for example, natural number's set and real number's set do not represent the same infinity.] For two disjoint sets A,B; the infinities they represent 'sum' to the infinity corresponding to union of A,B. Also, their 'product' is defined to be the infinity of the cartesian product of A,B. So, always obviously, if 'k' is such a infinity, k and 0(representing empty set) has product 0. If 'K','I' are two infinities or finities, for K$\geqslant$ I[This means there is a surjection from K to I], KI should be defined to be an infinity C so that I+C = K. But, the uniqueness of C depends on basic axioms, of course. Here base axioms give that max(I,1) = I+1, if I is an infinity. So your second answer should be K itself, for K an infinity.
You cannot say if I fail to recite
the umpteenth digit of PI,
Whether I'll live  or
whether I may, drown in tub and die.
the umpteenth digit of PI,
Whether I'll live  or
whether I may, drown in tub and die.
Re: Infinity*zero= ??
I don't think infinity^0=0. Can u explain how?Ishtiaque Ahmed wrote:The answer of question no.(1) will be 0 and question no.(2) will be infinity
Besides, as we define the index 0, infinity^0=infinity/infinity, which does not seem to make any sense unless u define how the infinity is reached (i also think that infinity is not a specific thing, it has different types, as said by fm) in which case limiting value can be taken. So normally saying, i think it will be undefined, coz we didn't define how the infinity was reached. And as said by Sowmitra via, I think infinity is not a 'specific' number. Seeing from that point also, infinity^0 goes undefined.
As for ques 2, since u do not say +infinity or infinity, i would take +infinity for now. Taking out a bucket of water from the sea doesn't change the sea level visually, so by approximation, we can observe that (+infinity)1=(+infinity). Also we can show this by contradiction.
Let (+infinity)1=p, where p is finite.
$\Rightarrow$ p+1=+infinity, which is a contradiction, so p cannot be finite. Hence p is infinite.
But (+infinity)1 not equal to (infinity), so p=+infinity
for infinity, p=infinity, which can be shown in a similar way