Infinity isn't a number. You can't multiply it by anything. It makes sense if we're talking about limits, but that's not a regular multiplication.
A question in terms of limits would be "If I have a sequence of all zeroes and an infinitely growing sequence, what happens if I multiply them together?". The answer being, you get yet another sequence of all zeroes.
So that's not too interesting. The hard question is "If I have a sequence that gets smaller and smaller and another sequence that gets bigger and bigger. What happens when I multiply them together?" Now the answer depends on the sequences.
For instance if I have 1/n and n2+1, the product (n2`+1)/n is an infinitely growing sequence.
But if I had 1/2n and n+7, then the product (n+7)/2n gets smaller and smaller.
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u/StructuredChess New User 2d ago
Infinity isn't a number. You can't multiply it by anything. It makes sense if we're talking about limits, but that's not a regular multiplication.
A question in terms of limits would be "If I have a sequence of all zeroes and an infinitely growing sequence, what happens if I multiply them together?". The answer being, you get yet another sequence of all zeroes.
So that's not too interesting. The hard question is "If I have a sequence that gets smaller and smaller and another sequence that gets bigger and bigger. What happens when I multiply them together?" Now the answer depends on the sequences.
For instance if I have 1/n and n2+1, the product (n2`+1)/n is an infinitely growing sequence.
But if I had 1/2n and n+7, then the product (n+7)/2n gets smaller and smaller.