Re: Bedeviled by the .999~ = 1 "debate"


CCCP1 wrote:
> I see this crop up from time to time on seemingly unrelated forums. People
> seem quite passionate about one side or the other. As one of the
> math-challenged, I've found that when this kind of pointless palaver occurs
> it usually indicates that the debate itself is somehow faulty (Muhammed Ali
> versus Bruce Lee, apples versus oranges, evolution versus creation).
>
> So without sparking this seemingly endless debate (I wouldn't get it
> anyway), is there any rug I can pull that might shut these people the hell
> up? :)

Nope.

Those who say 0.999... isn't equal to 1 are prone to language
involving time and change, like "it is always approaching,
getting closer and closer, but it never reaches 1."

Those who say 0.999... = 1 understand something about limits
of sequences, for instance that they are fixed constants and
not necessarily members of the sequence. 0.999... is the notation
for a particular limit. It has a particular value.

The gap seems unbridgable.

> IOW, is this the subject of actual mathematical discussion or is it a
> philosophical bauble tossed about purely for the enjoyment of tossing it
> about?

It's not the subject of mathematical discussion in the sense
of people who understand mathematics disagreeing. It's
a discussion between people who are comfortable with limits
and infinite sequences, and people who don't want to learn
the language and insist their intuitions are somehow
superior.

Obviously those who learned about limits started from
not knowing about limits. But to cross the bridge meant
accepting something, perhaps a willingness to accept a definition
as a starting point of an argument rather than a feeling.
Those on the 0.999... < 1 side generally don't accept
the definition of infinite sums either.

- Randy

.

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