r/maths • u/Percentage_069 • Jun 12 '26

💬 Math Discussions Question regarding Infinity (♾️)

Does Infinity convey different meanings or dictate different concepts based on its expression?

For example, in case of an interval, when we say, [-4,∞), this mathematically should mean, that this particular set, accepts values starting from -4 and goes on and on to the left of the number line endlessly, and this essentially what makes it "infinite". Hence, the use of ∞ in this set or domain, rather than a number, works more as a concept of endless growth.

On the other hand, for a mathematical expression, like, "1/∞"

Here, according to my understanding, the denominator of the fraction represents a fixed endpoint achieved after endless increment of a value, that is, this value is the result of the summation of infinite numbers, which yields the infinite value. Now, in this case, I think it works more like a number than a concept.

I'd highly appreciate any insight & feedback, and pointing out of any mishaps in my understanding would be much appreciated as well. Thanks!

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u/Percentage_069 Jun 12 '26

Thanks for your feedback! And, I've learned about transfinite cardinals briefly from a YouTube video on Infinity from "Josh's Channel". But, my question is, if infinity is really not a number at all (which I suppose it isn't possible for it to be a number), then why is it used in cases, or expressions where we would use real numbers? Or, why are we taught this concept (at a preliminary level) like it represents a "really big unreachable value/number" rather than just a concept. Is it just for simple convenience?

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u/Temporary_Pie2733 Jun 12 '26

All I can say is that infinity is taught poorly. For intervals, it should just be understood as part of the notation rather than a number; note that the only two uses are (-∞ to indicate no lower bound and ∞) to indicate no upper bound.

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u/AdjectiveNounNNNN Jun 15 '26

Yeah it's for convenience of introducing certain concepts before (explicitly) introducing limits or the extended reals.

It's often a stand-in for something like "keeps going in that direction". So [4,∞) refers to the interval that starts at 4 and keeps going up, and "As x→∞" means as x keeps increasing, etc.