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A very brief introduction to set-builder notation in informal language

Suppose we have a set of all colored objects. We want to represent this in set-builder notation. Let's look at the distinct components of set-builder notation and the distinct meaning they contribute to the structure. The reason we're going to do this is because it's very easy to become intimidated by the Gestalt structure, when in fact, as long as you understand each component of the structure, it's quite simple. We just need to take it one step at a time.

The following example is taken from Eric Steinhart's excellent book "More Precisely: The Math You Need To Do Philosophy."

"the set of..." - {...}

"the set of all x..." - {x...}

"the set of all x such that..." - {x | ... }

"the set of all x such that x is a colored object" - {x|x is a colored object}

The vertical line that separates the first x from the second means "such that." x is a variable and can be an element of any set. Simple! Practice writing set-builder notation with sets of different kinds of objects and this beginning notation will become familiar in no time.

Steinhart, Eric. "More Precisely: The Mathematics You Need To Do Philosophy." Broadview Press, 2009.