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> I think that saying that m "equals infinity" is probably a bit of a simplification. Yes, it is, I agree. For the limit example, one might instead say, "As m
by lutusp 11y ago
> I think that saying that m "equals infinity" is probably a bit of a simplification.
Yes, it is, I agree. For the limit example, one might instead say, "As m approaches infinity, the result approaches 1." By definition, limits approach their target values, they never equal them -- otherwise we would accept division by zero and similar things.
The other reason I agree is because infinity isn't a number. I'm guilty of compressing the lexical description of a limit to a ... ahem ... finite size.
> ... what is meant in the examples you gave, which are both limits.
One of my examples was an infinite sum, not a limit per se, but the same argument can be made, i.e. that infinity is addressed without being literally achieved.
- drdeca 11y agoI believe that infinite sums are usually defined in terms of limits, which is why I said that both examples were limits. > By definition, limits approach their target values, they never equal them -- otherwise we would accept division by zero and similar things. I think I would say that a convergent sequence (most of the time that one cares) does not ever reach the target value (though, eventually constant sequences do, but those aren't interesting), but that the limit of the convergent sequence is equal to / is the target value. As opposed to saying that "the limit approaches". The limit isn't the thing that changes with another thing, but the limit of some changing?