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ordertype

order type

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The answer ORDERTYPE (order type) has 0 possible clue(s) in existing crosswords.

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There are 9 letters in ORDERTYPE ( D²E¹O¹P³R¹T¹Y⁴ )

To search all scrabble anagrams of ORDERTYPE, to go: ORDERTYPE

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5 letters out of ORDERTYPE

4 letters out of ORDERTYPE

3 letters out of ORDERTYPE

DEE DEY DOE DOR DOT DRY DYE ERE ERR EYE ODE OPE OPT ORE ORT PED PEE PER PET POD POT PRO PRY PYE RED REE REP RET ROD ROE ROT RYE TED TEE TOD TOE TOP TOR TOY TRY TYE YEP YET YOD

2 letters out of ORDERTYPE

DE DO ED ER ET OD OE OP OR OY PE RE TO YE YO

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Definitions of order type in various dictionaries:

ORDER TYPE - In mathematics, especially in set theory, two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, whe...

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Order type description
In mathematics, especially in set theory, two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, when there exists a bijection (each element matches exactly one in the other set) f: X → Y such that both f and its inverse are strictly increasing (order preserving i.e. the matching elements are also in the correct order). In the special case when X is totally ordered, monotonicity of f implies monotonicity of its inverse. * For example, the set of integers and the set of even integers have the same order type, because the mapping * * * * n * ↦ * 2 * n * * * {\displaystyle n\mapsto 2n} * preserves the order and so does the inverse map, * * * * 2 * n * ↦ * n * * * {\displaystyle 2n\mapsto n} * . But the set of integers and the set of rational numbers (with the standard ordering) are not order isomorphic, because, even though the sets are of the same size (they are both countably infinite), there is no order-preserving bijective mapping between them. To these two order types we may add two more: the set of positive integers (which has a least element), and that of negative integers (which has a greatest element). The open interval (0,1) of rationals is order isomorphic to the rationals (since, for example, * * * * * y * = * * * * 2 * x * − * 1 * * * 1 * − * \| * * 2 * x * − * 1 * * \| * * * * * * * {\displaystyle \textstyle y={\frac {2x-1}{1-\vert {2x-1}\vert }}} * provides a strictly increasing bijection from the former to the latter); the half-closed intervals [0,1) and (0,1], and the closed interval [0,1], are three additional order type examples. * Since order-equivalence is an equivalence relation, it partitions the class of all ordered sets into equivalence classes.

Order type description

In mathematics, especially in set theory, two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, when there exists a bijection (each element matches exactly one in the other set) f: X → Y such that both f and its inverse are strictly increasing (order preserving i.e. the matching elements are also in the correct order). In the special case when X is totally ordered, monotonicity of f implies monotonicity of its inverse.
* For example, the set of integers and the set of even integers have the same order type, because the mapping
*
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* {\displaystyle n\mapsto 2n}
* preserves the order and so does the inverse map,
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* n
*
*
* {\displaystyle 2n\mapsto n}
* . But the set of integers and the set of rational numbers (with the standard ordering) are not order isomorphic, because, even though the sets are of the same size (they are both countably infinite), there is no order-preserving bijective mapping between them. To these two order types we may add two more: the set of positive integers (which has a least element), and that of negative integers (which has a greatest element). The open interval (0,1) of rationals is order isomorphic to the rationals (since, for example,
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* 2
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* {\displaystyle \textstyle y={\frac {2x-1}{1-\vert {2x-1}\vert }}}
* provides a strictly increasing bijection from the former to the latter); the half-closed intervals [0,1) and (0,1], and the closed interval [0,1], are three additional order type examples.
* Since order-equivalence is an equivalence relation, it partitions the class of all ordered sets into equivalence classes.

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