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Topic: to contruct reals as infinite decimals, do you need axiom of choice
Replies: 5   Last Post: Aug 18, 2013 5:46 PM

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Posts: 160
Registered: 11/29/05
to contruct reals as infinite decimals, do you need axiom of choice
Posted: Aug 18, 2013 3:33 AM
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Hi friends of sci.math. I have a question:

To construct real numbers as infinite decimals, do we need axiom of choice?
Say for example we are working in base B, then it seems we need to choose one of B natural numbers for an infinite number of positions at the same time.

For an arbitrary real number, I don't see how a "rule" to pick these digits can arise. It is random, so we must need axiom of choice, right?

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