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An assumption is a statement which is introduced into an argument, whose truth value is (temporarily) accepted as True.

In mathematics, the keyword let is often the indicator here that an assumption is going to be introduced.

For example:

Let $p$ (be true) ...

can be interpreted, in natural language, as:

Let us assume, for the sake of argument, that $p$ is true ...

Also defined as

Some authors use the term assumption to mean the antecedent of a conditional statement.

Also see