All formulas should be punctuated.  That includes displayed formulas.  They are part of your sentence structure.

To type text inside a formula, use the \text{...} command.  Don't let text be set in math italics.

We never "have that" or "get that" or "give that"; it is ungrammatical.  (Sorry, math nerds.)  Usually you can just cross it off and no harm is done; you might need to put in a comma.  The rest of the time you can usually cross off "that".  The remaining cases can be rewritten slightly if necessary.

NEVER USE \\ except where required by LaTeX syntax, barring very special circumstances.  Absolutely never use it to get a new line or blank line in text.  For the latter, use \bigskip, \medskip, \smallskip, or \vspace.

Do not use \noindent to prevent paragraph indentation, please.

Use \mid or : in set definitions.  Don't use |; it gives poor spacing.