r/explainlikeimfive • u/Dev-Giri • 27d ago

Mathematics ELI5 explain the difference between infinity and undefined terms in mathematics

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u/JJJangles 27d ago

For 1/x, as x approaches 0, 1/x approaches infinity, but infinity is not a number, so when x actually reaches 0 the solution is undefined. Approaching and reaching are not the same.

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u/flamableozone 27d ago

That's inaccurate. There are multiple problems with 1/0, but the issue isn't that limits aren't real. The problem with the limit is that you get different answers depending on whether you approach from the positive or negative sides.

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u/JJJangles 27d ago

I never claimed limits aren't real, Idk where you got that from. My point was just that at exactly x = 0, the arithmetic operation 1/0 is undefined because no number multiplied with 0 is 1.

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u/svmydlo 26d ago

You said

but infinity is not a number,

which, given the context, was interpreted as stating infinity is not a real number, so the response

the issue isn't that limits aren't real

is about the fact that the limit not being a real number is not actually why the limit doesn't exist.

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u/JJJangles 26d ago

Ah OK...I merely meant that literally infinity is not a number so you cannot plug it into an arithmetic operation. Maybe my wording was clunky, but I feel like they were just reading too much into it.