assume / presume

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Assume and presume are often used interchangeably. However, there’s a slight difference:

To assume means to take for granted as the basis of argument or action. There doesn’t have to be any proof for the assumption; it can be arbitrary. You can replace the word assume with suppose.

To presume means to assert that something is true without yet having complete evidence (hence the prefix “pre…”). However, there’s a belief that at least some evidence exists.

So there’s a stronger element of postulation or hypothesis in assume than in presume.

The nouns are presumption and assumption.

Yes:

Let’s assume that two users log in who both have the same name.

Yes:

To start the iterative process, let’s presume that a typical value for the average room temperature is 20° Celsius.