
Is infinity times zero = zero? - tosh
https://brilliant.org/wiki/is-infinity-times-zero-zero/
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Erlangen
I haven't touched analytical mathematics for a very long time, so my
understanding is quite rough now. Though the solution seems obvious, I hope
the proof gives more explanation.

1\. Is it OK to replace 0 with a function that approaches 0 at infinity? What
rules are in place for substitution?

2\. Is lim f(x) * lim g(x) equal to lim f(x)*g(x) ?

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simonblack
1\. No. In my opinion, zero can never equal non-zero.

Otherwise you could be 'only a little bit' pregnant.

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yongjik
This website presents a question that can be only answered by precisely
defining "infinity", and then shows an "answer" that just assumes (without
proof) a horde of stuff, including "lim (f * g) = (lim f) * (lim g)".

This is not a good way to learn math.

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simonblack

        infinity = 1+1+1+1 ..... +1+1
    
        infinity x 0 = (1x0)+(1x0)+(1x0) .... +(1x0)+1x0)
    
                     =  0   + 0   + 0    .... +  0  +  0
    
                     =  0

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simonblack
_Proof: We know ...._

That is a non-proof. Test it by finishing the sentence differently, as in
"Proof: We know ... that the world is flat."

