Set Notation

Abstract

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Set-Roster Notation

$$\{1,2,3\}$$ $$\{1,2,3,\dots ,100\}$$ $$\{1,2,3,\dots \}$$

• A Set may be specified by writing all of its elements between braces
• Symbol $\dots$ is called ellipsis and read “and so forth”

Set-Builder Notation

$$\{x\in U:P(x)\}$$ $$\{x\in U|P(x)\}$$

• The set of all x in U such that P(x) is true

Replacement Notation

$$\{t(x):x\in A\}$$ $$\{t(x)|x\in A\}$$

• For elements x in A, we apply the function t(x)