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This answer is going to sound a little weird, but I'm going to try not to use the word 'assume'.
This is making a statement about a variable or function or mathematical property without knowing if that is the correct statement. It is typically used in proofs. Often we will try to prove something is not true, so we assume that it is true. That means we make a statement that 'it is true'. Then proceed with if it's true, what else is true, or what will happen if this is true. If this leads to a contradiction, then you can say that the original assumption was incorrect.
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