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Q: A set of numbers placed at fixed distances?

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Is that the 'scale'?

It could be a ruler. Just a number line.

an ellipse.

The set of numbers which 3 does not belong is the set of even numbers.

Any well-defined set of numbers.

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Is that the 'scale'?

It could be a ruler. Just a number line.

A number line or, in 2 or more dimensions a grid.

In the branch of algebra called group theory, they are called equivalent classes or residual classes. They are generated with the fixed distance as the basis of the modulo relationship.

an ellipse.

Ocular scale

The set of all points in a plane for which the sum of the distances to two fixed points equals a certain constant. - APEX

No. Triangle numbers are a fixed set of numbers that can't be altered to make one certain number turn into a triangle number.

Sounds like an elliptical to me.

It is a set of metal wrights calibrated to measure fixed numbers of units of mass. They will be used to weight things in a mass balance.

You're trying to describe an "ellipse".

No, it is not.

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