What software can I use to typeset proofs for my class?

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I'm taking a class on proofs this semester. My first assignment is to prove propositions using axioms. Is there software I can use to type these mathematical symbols and equations?

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LaTeX is the gold standard for typesetting mathematics. Just install MiKTeX and you're ready to go. I personally prefer TeXmaker to the default editor (TeXworks) provided with MiKTeX, but there's plenty of options to chose from. Also, if you can't remember what the command is for some given symbol, detexify is very useful.