Fundamental axiom of analysis
- Fundamental axiom of analysis
In mathematics, the fundamental axiom of analysis (or simply the fundamental axiom) states:
:"Every non-decreasing sequence of real numbers which is bounded above tends to a limit."
The fundamental axiom may be shown to be equivalent to the least upper bound axiom, and the Bolzano-Weierstrass theorem: that is assuming any one of these three statements, one may prove both of the remaining two as theorems, following from the definitions and the single statement assumed to be true.
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