# Element

Element[x,dom]

or xdom asserts that x is an element of the domain dom.

Element[x,reg]

or xreg asserts that x is an element of the region reg.

Element[x1|x2|,dom]

asserts that all the xi are elements of dom.

Element[patt,dom]

asserts that any expression matching the pattern patt is an element of dom.

# Details

• xdom can be entered as x el dom or x[Element]dom.
• Element can be used to set up assumptions in Simplify and related functions.
• dom may be a numeric domain or a region in .
• Possible domains dom are:
•  Algebraics algebraic numbers Booleans Complexes complex numbers Integers integers Primes prime numbers Rationals rational numbers Reals real numbers
• Possible regions reg are defined by RegionQ.
• xdom if possible evaluates immediately when x is numeric.
• For a domain dom, {x1,x2,}dom is equivalent to (x1|x2|)dom.
• For a region reg, {x1,x2,}reg asserts that the point with coordinates x1,x2, belongs to reg.
• {x1,x2,}dom evaluates to (x1|x2|)dom if its truth or falsity cannot immediately be determined.

# Examples

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## Basic Examples(5)

Test whether is an element of the reals:

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Test whether the point belongs to the unit disk:

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Express domain membership for an expression:

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Assert that the point belongs to the unit ball:

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Use element assertions to integrate over a region:

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Or to optimize over a region:

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Enter using elem:

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