I am currently writing an Internal assessment about proving Squeeze Theorem, and could not find the exact notation for "for all x in some open interval containing c except possibly at c itself" It is a crucial part since the proof starts with this statement. Could anyone know the exact notation for this expression?
2026-04-07 00:47:13.1775522833
Mathematical notation of "for all x in some open interval containing c except possibly at c itself""
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You could describe it as the set $S$ where $S = I \setminus \{c\}$, where $I = \{x \in \mathbb R: a < x < b\}$ where $a < c < b$.
In the above $\setminus$ means the set difference: $A \setminus B = \{x \in A: x \notin B\}$.
This of course only gives you the interval which specifically does not include $c$; I'm not sure how you would write "not necessarily including $c$".