Proportional-to sign

The proportional-to sign ∝ leaves a constant unstated: y ∝ x means y = kx for a fixed k over the range being discussed.

IN FOCUS∝

PROPORTIONAL TO

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Meaning and context

The proportional-to sign ∝ leaves a constant unstated: y ∝ x means y = kx for a fixed k over the range being discussed.

How to use it

Follow the shorthand with a definition such as y = kx when the relationship must be computed. State which quantities remain constant.

Examples

Direct proportionality

y ∝ x means y = kx for a fixed k.

The constant is fixed over the domain being discussed.

Circle area

A ∝ r² for circles

Area scales with the square of radius; the constant is π.

Similar shapes, different characters

∞

Infinity

U+221E

The open shape of ∝ is not the closed infinity symbol.

Details
=

Equals sign

U+003D

An equality supplies the full expression, including any constant.

Sources and method

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