Any number multiplied by $0$ is $0$. Any number multiply by infinity is infinity or indeterminate. $0$ multiplied by infinity is the question. Answer with proof required.
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This problem can be considered using limits. – Grkxbvn Apr 22 '22 at 07:46
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The problem is the sentence "Any number multiplied by infinity is infinity or indeterminate" which is false.
Multiplication is an operation defined on real numbers. If you have two real numbers, $x$ and $y$, you can calculate $x\cdot y$ which is a real number.
$\infty$ is not a real number and you cannot multiply with it.
5xum
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What I would say is that you can multiply any non-zero number by infinity and get either infinity or negative infinity as long as it isn't used in any mathematical proof. Because multiplying by infinity is the equivalent of dividing by 0. When you allow things like that in proofs you end up with nonsense like 1 = 0. Multiplying 0 by infinity is the equivalent of 0/0 which is undefined. – PHP Guru Mar 02 '22 at 19:45
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And why is the result of any number not 0.0 multiplied by +/-Inf +/-Inf ? – Edison von Myosotis Sep 06 '23 at 12:51
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@EdisonvonMyosotis Your sentence is nonsensical. What do you mean by "the result of any number"? – 5xum Sep 06 '23 at 14:54
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0 multiplied by 0/0 (infinity) is 0 because the top and bottom zeros cancel out.. or are we seeing a breakdown of mathematical operations in this context? – Kieran Ryan Jun 02 '24 at 08:14
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Is it fair to say that mathematical operations on infinity have no effect? – Kieran Ryan Jun 02 '24 at 08:22
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@KieranRyan $0/0$ is not "infinity", it is not defined. So certainly, $0$ multiplied by it is not zero. – 5xum Jun 02 '24 at 18:36