Definition:Less Than (Real Numbers)
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Definition
Let $\R_{>0}$ denote the set of strictly positive real numbers.
Let $x, y \in \R$.
Then we write $x < y$ if and only if:
- $ y - x \in \R_{>0}$
and we say that $x$ is less than $y$.
Also see
Inequality iff Difference is Positive, where it is shown that this may be deduced from the Ordering Properties of Real Numbers.
Sources
- 2011: Robert G. Bartle and Donald R. Sherbert: Introduction to Real Analysis (4th ed.) ... (previous): $\S 2.1$