For a time the President received hundreds of them every day, most of them worthless.

For every rude word of Mr. Banks's the family had five in apology.

For every person on Taiwan, there are sixty in Mainland China.

For added strength, I also fastened a small block on each side of every frame and batten joint.

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

For every criterion which defines what something is, at the same time proclaims -- implicitly if not openly -- what that something is not.

For new galaxies to be created, Professor Bondi declares, it would only be necessary for a single hydrogen atom to be created in an area the size of your living room once every few million years.

For some reason, this ellipsis in the conversation spread until it swallowed up every other topic.

For example, " biweekly " can mean " fortnightly " ( once every two weeks – 26 times a year ), or " twice a week " ( 104 times a year ).

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** For every non-empty set S there is a binary operation defined on S that makes it a group.

For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬ AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets.

For Tarrou, plague is the destructive impulse within every person, the will and the capacity to do harm, and it is everyone's duty to be on guard against this tendency within themselves, lest they infect someone else with it.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

For Hume, every effect only follows its cause arbitrarily — they are entirely distinct from one another.

Professor Henry Higgins sings, " Look at her, a prisoner of the gutters / Condemned by every syllable she utters / By right she should be taken out and hung / For the cold-blooded murder of the English tongue.

For every 100 females there were 91. 4 males.

For every 100 females age 18 and over, there were 87. 4 males.

For every 100 females there were 105. 6 males.

For every 100 females age 18 and over, there were 97. 5 males.

For example, the division example above is surjective ( or onto ) because every rational number may be expressed as a quotient of an integer and a natural number.

For example, the BBC website, which had previously been called BBC Online, took on the BBCi brand from 2001, displaying an i-bar across the top of every page, offering a category-based navigation: Categories, TV, Radio, Communicate, Where I Live, A-Z Index, and a search.

For every 100 females there are 95. 6 males.

For every 100 females age 18 and over, there were 94. 7 males.

For example, in the Schrödinger picture, there is a linear operator U with the property that if an electron is in state right now, then in one minute it will be in the state, the same U for every possible.

For finite sets X, the axiom of choice follows from the other axioms of set theory.

For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers.

* For a finite field of prime order p, the algebraic closure is a countably infinite field which contains a copy of the field of order p < sup > n </ sup > for each positive integer n ( and is in fact the union of these copies ).

For example, intervals, where takes all integer values in Z, cover R but there is no finite subcover.

For example, the real line equipped with the discrete topology is closed and bounded but not compact, as the collection of all singleton points of the space is an open cover which admits no finite subcover.

For a finite group, the derived series terminates in a perfect group, which may or may not be trivial.

For an infinite group, the derived series need not terminate at a finite stage, and one can continue it to infinite ordinal numbers via transfinite recursion, thereby obtaining the transfinite derived series, which eventually terminates at the perfect core of the group.

For systems where the volume is preserved by the flow, Poincaré discovered the recurrence theorem: Assume the phase space has a finite Liouville volume and let F be a phase space volume-preserving map and A a subset of the phase space.

For continuous dynamical systems, the map τ is understood to be a finite time evolution map and the construction is more complicated.

* For every prime number p and positive integer n, there exists a finite field with p < sup > n </ sup > elements.

For example, Graham's number, though finite, is unimaginably larger than other well-known large numbers such as a googol, googolplex, and even larger than Skewes ' number and Moser's number.

For some finite n-valued logics, there is an analogous law called the law of excluded n + 1th.

Note: For any arbitrary number of propositional constants, we can form a finite number of cases which list their possible truth-values.

For instance, Fermat's little theorem for the nonzero integers modulo a prime generalizes to Euler's theorem for the invertible numbers modulo any nonzero integer, which generalizes to Lagrange's theorem for finite groups.

For a finite population, the population mean of a property is equal to the arithmetic mean of the given property while considering every member of the population.

For example, the real numbers with the standard Lebesgue measure are σ-finite but not finite.

For a non-relativistic system consisting of a finite number of distinguishable particles, the component systems are the individual particles.

For example, the usual decimal representation of whole numbers gives every whole number a unique representation as a finite sequence of digits.

For a nonzero vector of finite norm in, one can assume that is nonzero, or to fix ideas.

For example, a non-identity finite group is simple if and only if it is isomorphic to all of its non-identity homomorphic images, a finite group is perfect if and only if it has no normal subgroups of prime index, and a group is imperfect if and only if the derived subgroup is not supplemented by any proper normal subgroup.

For any luminosity from a given distance L ( r ) N ( r ) proportional to r < sup > a </ sup >, is infinite for a ≥ − 1 but finite for a < − 1.

For point masses the gravitational energy decreases without limit as they approach zero separation, and it is convenient and conventional to take the potential energy as zero when they are an infinite distance apart, and then negative ( since it decreases from zero ) for smaller finite distances.

For a set of polynomial equations in several unknowns, there are algorithms to decide if they have a finite number of complex solutions.