** Every surjective function has a right inverse.

Every bijective function g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;

Every space filling curve hits some points multiple times, and does not have a continuous inverse.

< li > Every positive definite matrix is invertible and its inverse is also positive definite.

Every real number has an additive inverse ( i. e. an inverse with respect to addition ) given by.

Every nonzero real number has a multiplicative inverse ( i. e. an inverse with respect to multiplication ) given by ( or ).

Every symplectic matrix is invertible with the inverse matrix given by

Every six rounds, a logical transformation layer is applied: the so-called " FL-function " or its inverse.

Every rotation Rot ( φ ) has an inverse Rot (− φ ).

Every reflection Ref ( θ ) is its own inverse.

Every animation in Trespasser is done using inverse kinematics.

Every join-semilattice is a meet-semilattice in the inverse order and vice versa.

* Every element of S has a unique inverse, in the above sense.

* Every element of S has at least one inverse ( S is a regular semigroup ) and idempotents commute ( that is, the idempotents of S form a semilattice ).

* Every group is an inverse semigroup.

* Every semilattice is inverse.

Every inverse semigroup S has a E-unitary cover ; that is there exists an idempotent separating surjective homomorphism from some E-unitary semigroup T onto S.

* Every cyclic shift and the inverse of a cyclically reduced word are cyclically reduced again.

Recall that a subsemigroup G of a semigroup S is a subgroup of S ( also called sometimes a group in S ) if there exists an idempotent e such that G is a group with identity element e. A semigroup S is group-bound if some power of each element of S lies in some subgroup of S. Every finite semigroup is group-bound, but a group-bound semigroup might be infinite.

Every F-inverse semigroup is an E-unitary monoid.

Every soldier in the army has, somewhere, relatives who are close to starvation.

Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every calculation has been made independently by two workers and checked by one of the editors.

Every retiring person has a different situation facing him.

Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

`` Every woman in the block has tried that ''.

: Every set has a choice function.

Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.

** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.

** Antichain principle: Every partially ordered set has a maximal antichain.

** Every vector space has a basis.

* Every small category has a skeleton.

* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).

** Every field has an algebraic closure.

** Every field extension has a transcendence basis.

** Every Tychonoff space has a Stone – Čech compactification.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.

Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.

Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.