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Topic: Continuity == Reals?
Replies: 7   Last Post: Aug 4, 2013 3:05 AM

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Posts: 40
Registered: 12/4/05
Continuity == Reals?
Posted: Aug 1, 2013 1:08 PM
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I was wondering if the definition of continuity (of a function) only makes sense over the reals or if it is possible over something like the rationals too.

Didn't the Greeks think that lines were rationals (or length of parts of lines) and that it was continuous?

I've heard and read phrases like "alpha can be a continuous variable" to refer to alpha being allowed to run over the reals or another uncountable set.

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