If F is algebraically closed and p ( x ) is an irreducible polynomial of F, then it has some root a and therefore p ( x ) is a multiple of x − a.

If one quantizes a real scalar field, then one finds that there is only one kind of annihilation operator ; therefore, real scalar fields describe neutral bosons.

If a player bets 1 unit on red, his chance of winning 1 unit is therefore 18 / 38 and his chance of losing 1 unit ( or winning-1 ) is 20 / 38.

If f is also surjective and therefore bijective ( since f is already defined to be injective ), then S is called countably infinite.

If such an eigenvalue is not stable, the dynamics of this eigenvalue will be present in the closed-loop system which therefore will be unstable.

If the level of an attractant remains high, the level of phosphorylation of CheA ( and therefore CheY and CheB ) will remain low, the cell will swim smoothly, and the level of methylation of the MCPs will increase ( because CheB-P is not present to demethylate ).

If a person is free to anger you at will, you have no control over your internal world, and therefore no freedom.

If the passer drops the ball before this moment it is a fumble and therefore a loose ball.

If therefore any prince or other layman shall arrogate to himself the right of disposition, control, or ownership of ecclesiastical goods or properties, let him be judged guilty of sacrilege.

If on the other hand Theorem 2 holds and φ is valid in all structures, then ¬ φ is not satisfiable in any structure and therefore refutable ; then ¬¬ φ is provable and then so is φ, thus Theorem 1 holds.

If the founders were to contact the Secret Chiefs, therefore, it had to be done on their own.

If hammering upwards gravity will reduce the acceleration during the hammer stroke and therefore reduce the energy delivered with each blow.

If the domain is the real numbers, then each element in Y would correspond to two different elements in X (± x ), and therefore ƒ would not be invertible.

The Council of Trent decreed: " If anyone shall say that a man once justified can sin no more, nor lose grace, and that therefore he who falls and sins was never truly justified ; or, on the contrary, that throughout his whole life he can avoid all sins even venial sins, except by a special privilege of God, as the Church holds in regard to the Blessed Virgin: let him be anathema.

If, on the other hand, a currency is under-valued, its exports will become cheaper and therefore more competitive internationally.

If μ is an unknown constant and W is random noise with probability density, then has probability density and is therefore a location family ..

If a commodity's value is not the same as its price, and therefore the magnitudes of each likely differ, then what is the relation between the two, if any?

Cafiero explains in Anarchy and Communism ( 1880 ) that private property in the product of labor will lead to unequal accumulation of capital and, therefore, the reappearance of social classes and their antagonisms, and thus the resurrection of the state: " If we preserve the individual appropriation of the products of labour, we would be forced to preserve money, leaving more or less accumulation of wealth according to more or less merit rather than need of individuals.

# If G is any group acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.

If they believe in determinism, they will therefore believe free will to be an illusion, a position known as Hard Determinism.

If, therefore, the legislature pass any laws, inconsistent with the sense the judges put upon the constitution, they will declare it void.

If ( V, ‖·‖) is a normed vector space, the norm ‖·‖ induces a metric ( a notion of distance ) and therefore a topology on V. This metric is defined in the natural way: the distance between two vectors u and v is given by ‖ u − v ‖.

If a deity's power is to be great, it must therefore be over beings that have at least some of their own defenses and agenda.

Psychological egoism has been accused of being circular: " If a person willingly performs an act, that means he derives personal enjoyment from it ; therefore, people only perform acts that give them personal enjoyment.

If we can prevent something bad without sacrificing anything of comparable significance, we ought to do it ; absolute poverty is bad ; there is some poverty we can prevent without sacrificing anything of comparable moral significance ; therefore we ought to prevent some absolute poverty.

If he had had a son, he would tell him, `` Gather ye rosebuds while ye may This same flower that smiles today tomorrow will be dying ''.

If ye break faith with us who die

The text " If ye break faith ~ we shall not sleep " and " Buy Victory Bonds " are written at the top and bottom respectively.

Not you ye proud, impute to these the blame If Afric's sons to genius are unknown, For Banneker has prov'd they may acquire a name, As bright, as lasting, as your own.

If any of you know cause or just impediment why these persons should not be joined together in Holy Matrimony, ye are to declare it.

After the meal, it is recorded that Jesus washed their feet, and gave them the following mandatum or command: " If I then, your Lord and Master, have washed your feet, ye also ought to wash one another's feet.

If thou lend money to any of My people, even to the poor with thee, thou shalt not be to him as a creditor ; neither shall ye lay upon him interest.

Too often we forget to look at his compositions for other monarchs ; several of Tallis's anthems written in Edward's reign such as his If ye love me, ought to be considered on the same level as his Elizabethan works.

If he called them gods, unto whom the word of God came, and the scripture cannot be broken ; Say ye of him, whom the Father hath sanctified, and sent into the world, Thou blasphemest ; because I said, I am the Son of God?

Some believe Paul wrote the entire book of Galatians attacking circumcision and requiring the keeping of Jewish law by Christians, saying in chapter five: " If ye be circumcised, Christ shall profit you nothing.

In the Gospel of Jesus is reported as giving this response to those who criticized him for healing on Sabbath: " If a man on the sabbath day receive circumcision, that the law of Moses should not be broken ; are ye angry at me, because I have made a man every whit whole on the sabbath day?

If ye know these things, happy are ye if ye do them.

If ye barn Auchindoun, Huntly he will heid ye

If the suffix is being appended to a name ending in й ( y ) or a soft consonant, the initial o becomes a ye (- евич-yevich and-евна-yevna ).

If a woman were killed, one would have to pay half of the regular fine ( called “ poluvir ’ ye ”, half of “ vira ”).

If ye are faithful, ye shall assemble yourselves together to rejoice upon the land of Missouri, which is the land of your inheritance, which is now the land of your enemies.

" Aaron argued with himself, saying: If I say to Israel, Give ye to me gold and silver, they will bring it immediately ; but behold I will say to them, Give ye to me the earrings of your wives and of your sons, and forthwith the matter will fail, as it is said, " And Aaron said to them, Break off the golden rings.

“ If ye think good, give me my price ;

He was buried in his beloved garden, and his epitaph is still there today: " If ye seek his monument, look around ".