Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:

Every positive number a has two square roots:, which is positive, and, which is negative.

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

Every positive integer appears exactly once somewhere on this list.

Every positive real number x has a single positive nth root, which is written.

Every non-zero number x, real or complex, has n different complex number nth roots including any positive or negative roots, see complex roots below.

Every line of a GEDCOM file begins with a level number where all top-level records ( HEAD, TRLR, SUBN, and each INDI, FAM, OBJE, NOTE, REPO, SOUR, and SUBM ) begin with a line with level 0, while other level numbers are positive integers.

Every positive rational number can be represented by an Egyptian fraction.

* Every subset of may be covered by a finite set of positive orthants, whose apexes all belong to

* Every positive integer can be written as the sum of 73 or fewer sixth powers ( see Waring's problem ).

Every positive integer is the sum of at most 37 fifth powers ( see Waring's problem ).

* Every positive integer except 1 is a PV number.

Every positive integer can be expressed as the sum of at most 19 fourth powers ; every sufficiently large integer can be expressed as the sum of at most 16 fourth powers ( see Waring's problem ).

A finitely-generated abelian group is indecomposable if and only if it is isomorphic to Z or to a factor group of the form for some prime number p and some positive integer n. Every finitely-generated abelian group is a direct sum of ( finitely many ) indecomposable abelian groups.

Every C *- algebra has an approximate identity of positive elements of norm ≤ 1 ; indeed, the net of all positive elements of norm ≤ 1 ; in A with its natural order always suffices.

Every positive rational number can be expanded as an Egyptian fraction.

Every positive integer is the sum of at most 143 seventh powers ( see Waring's problem ).

Every residue class in this group contains exactly one square free integer, and it is common, therefore, only to consider square free positive integers, when speaking about congruent numbers.

Every positive rational number q may be expressed as a continued fraction of the form

* Revised Code of Washington 9. 12. 010: " Every person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state, with intent thereby to distress or harass a defendant in the suit, or who serves or sends any paper or document purporting to be or resembling a judicial process, that is not in fact a judicial process, is guilty of a misdemeanor ; and in case the person offending is an attorney, he or she may, in addition thereto be disbarred from practicing law within this state.

Every SE must be registered in the State where it has its registered office, in a register designated by the law of that State.

Every law, every letter, every syllable of inflection in the different languages was illustrated by an almost exhaustive mass of material, and it has served as a model for all succeeding investigators.

# Moral law of karma: Every action ( by way of body, speech, and mind ) will have karmic results ( a. k. a. reaction ).

The moral law stands on an entirely different foundation from the ceremonial or ritual law .... Every part of this law must remain in force upon all mankind and in all ages.

Every vibrating object tends to maintain its plane of vibration if its support is rotated, a result of Newton's first law.

Maxwell Fyfe brought up Raeder's order of 15 October 1939, which read: " Measures which are considered necessary from a military point of view will have to be carried out, even if they are not covered by existing international law ... Every protest from neutral powers will have to be turned down ... The more ruthlessly economic warfare is waged ... the sooner the war will come to an end ".

The Body of Liberties adopted in 1641 by the Massachusetts Bay colonists states, “ Every married woman shall be free from bodily correction or stripes by her husband, unless it be in his own defense from her assault .” In the United States, legal decisions in Mississippi ( 1824 ) and North Carolina ( 1868 and 1874 ) make reference to — and reject — an unnamed " old doctrine " or " ancient law " by which a man was allowed to beat his wife with a stick no wider than his thumb.

Every case in which a court discovers a violation of the Charter would therefore require a section 1 analysis to determine if the law can still be upheld.

The International Committee of the Red Cross 1958 Commentary on 1949 Geneva Convention IV Relative to the Protection of Civilian Persons in Time of War states: " Every person in enemy hands must have some status under international law: he is either a prisoner of war and, as such, covered by the Third Convention, a civilian covered by the Fourth Convention, or again, a member of the medical personnel of the armed forces who is covered by the First Convention.

Every fellow was to study theology, save for two who were to study astronomy, two civil law, four canon law, and two medicine ; all fellows save those studying secular subjects were obliged to take Holy Orders and become priests, on pain of expulsion.

Equity has come not to destroy the law but to fulfill it, to supplement it, to explain it .” Every jot & every title of law was to be bayed, but when all this had been done yet something might be needed, something that equity would require & that was added by equity.

Every year, by law and by custom, we meet here to threaten the world.

Every state of the United States recognizes corporations sole under common law, and fifteen states have specific statutes that stipulate the conditions under which that state recognizes the corporations sole that are filed with that state for acquiring, holding, and disposing of title for church and religious society property.

: Every law or resolution having the force of law, shall relate to but one subject, and that shall be expressed in the title.

Every lawn mower sold in the US since 1982 has an " operator-presence " device, which by law must stop the blades within 3 seconds after the user lets go of the controls.

Every Afghan shall have the right, according to provisions of law, to print and publish on subjects without prior submission to state authorities.

Every score within five years is reported to law schools during the application process, as well a separate average of all scores on record.

*" Every denunciation of existing law tends in some measure to increase the probability that there will be violation of it.

Every path from back door to barn was covered by a grape-arbor, and every yard had its fruit trees.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every pitch in the game brought forth a howl from the enraptured audience and every fly ball the visitors dropped ( and because their right fielder was still a little fuzzy from drink, they dropped many ) called forth yelps of derision.

Every man in every one of these houses is a Night Rider.

** 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.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.

Every cleric in Holy Orders and every member of a religious order must publicly join in or privately read aloud ( i. e. using the lips as well as the eyes — it takes about two hours in this way ) the whole of the Breviary services allotted for each day.

Every retraction is an epimorphism, and every section is a monomorphism.

Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.

Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.

Every corporation, whether financial or union, as well as every division of the administration, were set up as branches of the party, the CEOs, Union leaders, and division directors being sworn-in as section presidents of the party.

Every gun that is made, every warship launched, every rocket fired signifies, in the final sense, a theft from those who hunger and are not fed, those who are cold and are not clothed.

Every mental phenomenon, every psychological act, has a content, is directed at an object ( the intentional object ).

Every step had been carefully planned, every calculation meticulously done.

" More immediately, though, he called for a massive build-up of U. S. arms production: " Every realist knows that the democratic way of life is at this moment being ' directly assailed in every part of the world … The need of the moment is that our actions and our policy should be devoted primarily — almost exclusively — to meeting this foreign peril.

Every continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).

Every galaxy of sufficient mass in the Local Group has an associated group of globular clusters, and almost every large galaxy surveyed has been found to possess a system of globular clusters.

Every valley, every cliff, to my look is beautiful.

Every seminorm on V ( in particular, every norm on V ) is sublinear.

Every little change in every little property would mean the whole thing is destroyed.