I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
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You're thinking of a different calculus problem in this case we are comparing the growth rate of
100*\infty vs \infty. In calculus, you cannot accelerate the growth of \infty. If you put\infty / \inftyyour answer will beundefined(you can double check with Wolfram), similarly, if you put100*\infty / \infty, you will also getundefined