4.3.6 - Claimed Equality but Only Proved Subset
bschneidr opened this issue · comments
Ben Schneider commented
In this proof, you claim that
$ D_r \circ D_s = \{(a,b) \in R \times R \mid |a-b| < s + r\}$
but you only proved that
$ D_r \circ D_s \subseteq \{(a,b) \in R \times R \mid |a-b| < s + r\}$
To prove your claim, you would need to also prove the following:
$ \{(a,b) \in R \times R \mid |a-b| < s + r\} \subseteq D_r \circ D_s $
I'm not sure whether this can be proved, but I'll submit a pull request if it can be proved or a counterexample can be found.
Sibi Prabakaran commented
Thanks for the catch. Would be glad to accept PR. :)