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# fix

In mathematical statements, mathematical objects such as points and numbers are described as being *fixed*. A possible meaning for this usage is that the mathematical object in question is not allowed to vary throughout the statement or proof (or, in some cases, a portion thereof). Although a fixed object typically does not vary, it is almost always arbitrary. This may seem paradoxical, but it is quite logical: An object is chosen arbitrarily, then it is never allowed to vary. See the entry betweenness in rays for an example of this usage.

The usage of the words *fix* and *fixed* may also mean that a mapping sends the mathematical object to itself. These two usages are technically not the same. The former usage (described in the previous paragraph) states a property of the mathematical object in question and is always either part of an implication (as in “If $x\in\mathbb{R}$ is fixed, then…”) or a command made by the author to the reader (as in “Let $x\in\mathbb{R}$ be fixed.” and “Fix $x\in\mathbb{R}$.”). The latter usage (described in this paragraph) states a property of a mapping and may or may not be part of a conditional statement or a command. The word “fixes” *always* refers to this usage (as in “Note that $f$ fixes $x$.”). See the entry fix (transformation actions) for a further explanation of the latter usage.

## Mathematics Subject Classification

03-00*no label found*03F07

*no label found*

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## Comments

## MSC's on fix

I am uncertain about the MSC's on this entry and would greatly appreciate any advice you have to offer.

Warren