Re: .999... = 1

Ken Quirici wrote: 
I.e., mathematics would be hopelessly bogged down if you didn't
replace any Cauchy sequence approaching a limit by that limit and
consider yourself done.


That's pretty much it: you can think of a real number as
precisely being an equivalence class of Cauchy sequences
of rationals.

However, to me, .99999... represents a sequence that tends to 1,
rather than 1.


OK, so it's a sequence of rationals that tends to 1. That
means that (as a real number) it *is* (a representative of)
1. (Of course, '1' gets used in two slightly different ways
there.)

Hope this makes some sense. I can't wrap my mind around the
notation .99999.... = 1. It's apples and oranges, at least
to my benighted mathematical logic.


Once you get used to it, it's no worse than

0.5 = 1/2

Not so much apples with oranges as gala with cox's pippins.

One aspect of mathematical maturity is thinking of things
in lots of different ways, and using whichever way of
thinking about them is most efficient in a given context.
.

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