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Every particular finite line, surface, or solid which may possibly be the object of our thought is an idea existing only in the mind, and consequently each part of it must be perceived.
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Every and particular
Every cladogram is based on a particular dataset that was analyzed with a particular method.
Every single thermodynamic system exists in a particular state.
Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.
Every seminorm on V ( in particular, every norm on V ) is sublinear.
Earlier books such as What Every Girl Should Know ( Margaret Sanger, 1920 ) and A Marriage Manual ( Hannah and Abraham Stone, 1939 ) had broken the silence in which many people, women in particular, had grown up in.
Every other bishop is charged with the care of his particular flock, the Roman pontiff with that of the whole Church.
Every salsa musician must know how their particular part fits with clave, and with the other parts of the ensemble.
Every man being organized in a particular way has, of necessity, an aim, the fulfilment of which is good ; and he has faculties for accomplishing it, directed by reason.
( Every diocese is a particular Church, but not an autonomous one in the sense in which the word is applied to these 22 Churches.
Every human action, however, is singular, contingent and takes place in particular circumstances.
Every User RPL command checks the stack for its particular arguments and returns an error if they are incorrect or not present.
It was observed twenty years later that " Every so often, there comes to light a document revealing the foresight of a public servant who grasped the full consequences and implications of a particular government measure or policy.
Every all-nighter at Wigan Casino ended with the playing of three well-known northern soul songs with a particular going home theme.
Every period is followed by a clinical exam regarding the student's knowledge in that particular specialty.
Every blister that contains a Wizard includes a free Incantation Rules Booklet as well as cards that describe magic items and special spells particular to each.
" Every man is, in his own particular way, a scientist ," said Kelly, in that he is always building up and refining theories and models about how the world works so that he can anticipate events.
Every single string produces its own cascading range of harmonics and, at the same time, builds up a particular resonance.
Every album focuses on a particular color and usually involves themes of small town rural America.
( 1 ) Every individual is equal before and under the law and has the right to the equal protection and equal benefit of the law without discrimination and, in particular, without discrimination based on race, national or ethnic origin, colour, religion, sex, age or mental or physical disability.
Every Maiden considers him a member of the family, though particular role ( son, older brother, younger brother ) varies from woman to woman.
* Every character value is a sum of n m < sup > th </ sup > roots of unity, where n is the degree ( that is, the dimension of the associated vector space ) of the representation with character χ and m is the order of g. In particular, when F is the field of complex numbers, every such character value is an algebraic integer.
Every joseki should be used as a specific tool that leaves the board in a particular shape.
One particular ad line read " Every normal skin needs these two creams ".
; Sherrington's First Law: Every posterior spinal nerve root supplies a particular area of the skin, with a certain overlap of adjacent dermatomes.
Every and finite
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
# Every open cover of A has a finite subcover.
* Countably compact: Every countable open cover has a finite subcover.
# Every finite and contingent being has a cause.
Every finite simple group is isomorphic to one of the following groups:
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.
Every finite tree structure has a member that has no superior.
Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.
* Every finite tree with n vertices, with, has at least two terminal vertices ( leaves ).
Every finite group of exponent n with m generators is a homomorphic image of B < sub > 0 </ sub >( m, n ).
Every known Sierpinski number k has a small covering set, a finite set of primes with at least one dividing k · 2 < sup > n </ sup >+ 1 for each n > 0.
Every finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by linear algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space.
: Every oriented prime closed 3-manifold can be cut along tori, so that the interior of each of the resulting manifolds has a geometric structure with finite volume.
Every finite or bounded interval of the real numbers that contains an infinite number of points must have at least one point of accumulation.
Every field of either type can be realized as the field of fractions of a Dedekind domain in which every non-zero ideal is of finite index.
Every process involving charged particles emits infinitely many coherent photons of infinite wavelength, and the amplitude for emitting any finite number of photons is zero.
Every finite group has a composition series, but not every infinite group has one.
* Every finite or cofinite subset of the natural numbers is computable.
* Every subset of may be covered by a finite set of positive orthants, whose apexes all belong to
* Every finite subextension of F / k is separable.
Every finite ordinal ( natural number ) is initial, but most infinite ordinals are not initial.
* Every finite-dimensional central simple algebra over a finite field must be a matrix ring over that field.
* Every commutative semisimple ring must be a finite direct product of fields.
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