Post History
#2: Post edited
by
Peter Taylor
·
2023-11-03T08:54:20Z (about 1 year ago)
Use conventional placement of binding operators
$|a-b|<\epsilon \; \forall ε >0 \iff a=b$ vs. $a \le b + ε \; \forall ε >0 \iff a \le b$
- $\left(\forall \varepsilon >0: |a-b| < \varepsilon\right) \iff a=b$ vs. $\left(\forall \varepsilon > 0: a \le b + \varepsilon \right) \iff a \le b$
How does [$|a-b|< ε \; \forall ε >0 \iff a=b$](https://math.stackexchange.com/q/3436553) relate to [$a \le b + ε \; \forall ε >0 \iff a \le b$](https://math.stackexchange.com/q/679038)? Does one equivalence imply the other? Are they equivalent?I feel they're related because they're both equivalences, they both involve ε > 0, and they both involve inequalities.
- How does $\left(\forall \varepsilon >0: |a-b| < \varepsilon\right) \iff a=b$ relate to $\left(\forall \varepsilon > 0: a \le b + \varepsilon \right) \iff a \le b$? Does one equivalence imply the other? Are they equivalent?
- I feel they're related because they're both equivalences, they both involve $\varepsilon > 0$, and they both involve inequalities.
#1: Initial revision
by
YorkTech
·
2023-11-01T21:33:11Z (about 1 year ago)
$|a-b|<\epsilon \; \forall ε >0 \iff a=b$ vs. $a \le b + ε \; \forall ε >0 \iff a \le b$
How does [$|a-b|< ε \; \forall ε >0 \iff a=b$](https://math.stackexchange.com/q/3436553) relate to [$a \le b + ε \; \forall ε >0 \iff a \le b$](https://math.stackexchange.com/q/679038)? Does one equivalence imply the other? Are they equivalent? I feel they're related because they're both equivalences, they both involve ε > 0, and they both involve inequalities.