Consider $A=(0,1)∪\{2\}$ and $B=(0,1)∪\{3\}$. Both sets have maxima, $2$ and $3$ respectively. But $A∩B=(0,1)$ which has no maximum.
How can we say that $A∩B=(0,1)$ does not have any maximum. Wouldn't it be $1$ ?
2026-04-02 22:34:22.1775169262
Is A∩B has Maximum?
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$1$ is not a max, since the interval $(0,1)$ is open, this means, in particular that $1$ is not in the set. This set has no max, but it has an upper bound.