By mathematical context, is there something undifined by mathematics?
Sure. If you are talking pure mathematics, Gödels famous theorem states that there are some true statements that cannot be proved (and some false statements that cannot be disproved).
So what? Mathematics isn't physics - or chemistry or... Mathematics is a tool to help you describe some real-world phenomena.
It is not at all clear what you mean by "undefined by mathematics". As Svein said, given any axiom system there exist statements that can be phrased in that system but neither proven nor disproven. But you said "undefined", not "proved".
1/0 is undefined.
Any number divided by zero is undefined.
More to the point, statements in mathematics or logic are only defined if they are well-formed formulae (wffs for short). So, I can write [tex]x\forall (\longrightarrow (\wedge ) \emptyset[/tex]all of which are mathematically well defined symbols, but since the above atrocity is not a wff, it is undefined.
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