Definition:Assumption

Definition

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

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

Examples

Arbitrary Example

The assumption:

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

• 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.

• Rule of Assumption

• Results about assumptions can be found here.

Sources

• 1965: E.J. Lemmon: Beginning Logic ... (previous) ... (next): $\S 1.2$: Conditionals and Negation
• 1966: Isaac Asimov: Understanding Physics ... (previous) ... (next): $\text {I}$: Motion, Sound and Heat: Chapter $1$: The Search for Knowledge: The Greek View of Motion
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): assumption
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): assumption
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): assumption