In mathematics, the keyword let is often the indicator here that an assumption is going to be introduced.
- 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
- Definition:Axiom: a statement whose truth (in a particular mathematical context) is accepted beyond doubt or question.
- Definition:Premise: a statement which is specifically used for the purpose of deriving a conclusion.