502
Not that limit (lemmy.world)
submitted 9 months ago by to c/science_memes@mander.xyz
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[–] 51 points 9 months ago (11 children)

It’s been a while… but isn’t that negative?

Or is there some default given of which side it’s approaching from.

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  • [–] 26 points 9 months ago* (last edited 9 months ago)

    (Just including the graph for reference. I'm not sure it helps with proper description or the answer the teacher was asking for, but you can see that from one direction it goes negative as you approach 8 and from the other it goes to positive infinity.)

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  • [–] 35 points 9 months ago* (5 children)

    I think it is not defined. It has a limes from the left (- inf) and limes from the right (+ inf) but no two-sided limes.

    Edit: wolframalpha agrees but I don't know for sure

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  • [–] 18 points 9 months ago (3 children)

    It has a limes from the left… and limes from the right…

    Is that the Tootsie Roll Theorem?

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  • [–] 12 points 9 months ago (3 children)

    I have a BA in Mathematics. The limit is indeed determined by the direction you approach the limiting value.

    When given without specification, the limit is implied to come from the left, meaning it increases towards the limiting value, which is why you see +inf.

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  • [–] 6 points 9 months ago* (2 children)

    This is just not true. The normal limit we have here means a limit would have to exist from both directions and they should be equal. They're not, so the limit doesn't exist.

    One-sided limits would be denoted by x -> 5– and x -> 5+ or similar.

    PS: in complex analysis, there is no distinction between +infty and -infty, so there it would be correct to say the function has limit infty at 5.

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  • [–] 3 points 9 months ago

    In my experience with maths, there's a whole bunch of different conventions all over the place, so it might've genuinely been how they were taught, even if you were taught differently...

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