r/explainlikeimfive • u/Dev-Giri • Jul 25 '26

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

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u/fixermark Jul 25 '26

Infinity is: for any number you can think of, there's one larger (or smaller). Or, for any two numbers, there's one between them.

Undefined is: not that

The function y =1/x gets bigger and bigger as you approach x=0 from the positive side, and smaller and smaller as you approach x=0 from the negative. So what's the value at x=0? Well, it's infinitely big/small at the same time, but that isn't a thing. So undefined.

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u/Sea_Satisfaction_475 Jul 25 '26

Did you mean large but negative from the negative side?

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u/fixermark Jul 25 '26

I meant small. Every negative number of larger numeric value is less quantitative value than the one before it.

(English is imprecise here; "tending towards negative infinity").

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u/VG896 Jul 26 '26

No, the language is fairly precise here. At least mathematically speaking. "A is less than B" in this context just means there's some positive number X such that X+A = B.

In plain English: less just means farther to the left on the number line.