A field extension M of K is called normal iff whenever an irreducible polynomial f(x) in K[x] has a zero in M then it can be factorised into linear factors in M[x], that is we can write f(x)=a(x-b₁)...(x-b₀), for some a,b_i in M.

For example, the fundamental theorem of algebra tells us that C is a normal extension of Q.

For those in doubt...

"Normal" does exist.

There are some under the delusion that social normalcy does not exist. These people have usually been outcast by the same society that they so hate. By denying the existance of normalcy, one is avoiding it just as a small animal avoids its predator by closing its eyes ("If I can't see it, it can't see me").

People who claim that there is no "normal" often wish to be normal themselves. The only alternative, being abnormal, is seen as something dirty and to be hated. This is not the case. Being abnormal is very fun. Normal people just sit bored when at a party that has no familiar faces. Abnormal people will get up and dance, yelling at people to join them. Sure, you've made a fool of yourself, but you've also made a lot of people laugh. Being abnormal can be fun.

How do I know that normal exists? Well, I just look at society. Maybe the norm is not strictly defined, but I definitely know that coating your face with flour while screaming the names of all your friends is not normal. Wearing jeans at a casual party is normal. Normalcy is more of a "vibe" than predefined values for social values, but that does not mean that it doesn't exist.

Anyways, you look pretty stupid denying the existence of something we see every day.

Nor"mal (?), a. [L. normalis, fr. norma rule, pattern, carpenter's square; prob. akin to noscere to know; cf. Gr. well known, gnomon, also, carpenter's square: cf. F. normal. See Known, and cf. Abnormal, Enormous.]

1.

According to an established norm, rule, or principle; conformed to a type, standard, or regular form; performing the proper functions; not abnormal; regular; natural; analogical.

Deviations from the normal type. Hallam.

2. Geom.

According to a square or rule; perpendicular; forming a right angle. Specifically: Of or pertaining to a normal.

3. Chem.

Standard; original; exact; typical

. Specifically: (a) Quantitative Analysis

Denoting a solution of such strength that every cubic centimeter contains the same number of milligrams of the element in question as the number of its molecular weight

. (b) Chem.

Denoting certain hypothetical compounds, as acids from which the real acids are obtained by dehydration; thus, normal sulphuric acid and normal nitric acid are respectively S(OH)6, and N(OH)5

. (c) Organ. Chem.

Denoting that series of hydrocarbons in which no carbon atom is united with more than two other carbon atoms; as, normal pentane, hexane, etc. Cf. Iso-.

Normal equations Method of Least Squares, a set of equations of the first degree equal in number to the number of unknown quantities, and derived from the observations by a specified process. The solution of the normal equations gives the most probable values of the unknown quantities. -- Normal group Geol., a group of rocks taken as a standard. Lyell. -- Normal place (of a planet or comet) Astron., the apparent place in the heavens of a planet or comet at a specified time, the place having been determined by a considerable number of observations, extending perhaps over many days, and so combined that the accidental errors of observation have largely balanced each other. -- Normal school, a school whose methods of instruction are to serve as a model for imitation; an institution for the training of teachers.

Syn. -- Normal, Regular, Ordinary. Regular and ordinary are popular terms of well-known signification; normal has now a more specific sense, arising out of its use in science. A thing is normal, or in its normal state, when strictly conformed to those principles of its constitution which mark its species or to the standard of a healthy and natural condition. It is abnormal when it departs from those principles.

 

© Webster 1913.

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Nor"mal (?), n. [Cf. F. normale, ligne normale. See Normal, a.]

1.

(Geom.) Any perpendicular.

2. Geom.

A straight line or plane drawn from any point of a curve or surface so as to be perpendicular to the curve or surface at that point.

⇒ The term normal is also used to denote the distance along the normal line from the curve to the axis of abscissas or to the center of curvature.

 

© Webster 1913.