They are usually not valid.
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no
Math that requires you to visualize higher dimensional graphs. It is often less algebra and more pictures of geometry.
In math terms, it is more or less to make something sound reasonable; but in a way that is less formal than a proof.
true
A math dictionary (or a mathematics dictionary) is usually a dictionary of the definitions of common mathematical terms, formulae and examples of common diagrams and pictures for the uninitiated or those learning math.