How to I show that every infinite string of decimal digits corresponds to a unique real number using the completeness axiom? I am suppose to somehow construct a bounded set with supremum but do not know how..this problem seems to be way beyond me.
How to I show that every infinite string of decimal digits corresponds to a unique real number using the completeness axiom? I am suppose to somehow construct a bounded set with supremum but do not know how..this problem seems to be way beyond me.
I don't understand the question.
Are you trying to show that if there is an "infinite" decimal expansion for ? If you're counting things like then you're answer lies in considering a sequence of rational numbers which converges to
If you are given an infinite decimal expansion it clearly (I hope ) represents a real number and if then (foregoing convergence issues for now)
I can't say much more from there.