## Infinity*zero= ??

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oro
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### Infinity*zero= ??

1) Infinity*zero= ??
2) Infinity -1= ??(I was thinking that, if it is one less than infinity then is it truly infinity??? )

Sidharth
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### Re: Infinity*zero= ??

I think no.(1) will be 0 and no.(2) will be infinity

Ishtiaque Ahmed
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### Re: Infinity*zero= ??

The answer of question no.(1) will be 0 and question no.(2) will be infinity

sowmitra
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### Re: Infinity*zero= ??

I don't think Infinity is a number... it is a concept...
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Fm Jakaria
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### 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], K-I 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.
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Rabeeb
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### Re: Infinity*zero= ??

Ishtiaque Ahmed wrote:The answer of question no.(1) will be 0 and question no.(2) will be infinity
I don't think infinity^0=0. Can u explain how?

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