Another bit of dated slang. In the 80's, "radical" was used to connote extreme excellence or eliteness.To be radical was to be cool raised to the second power. Often abbreviated as "rad" or (more commonly) "fucking rad". Now primarily used by old farts trying to look young or young farts being smartassed and ironic.

For example:

Radical blouse, Kathie! Is it Jordache?

From Latin radix (root), in Chinese script, a radical is a root character, i.e., one of 214 basic characters from which all other Chinese characters are derived.

For example, to find a Chinese character in Mathews' Chinese-English Dictionary (and probably other Chinese dictionaries), you first need to identify its radical, then find the character in the radical index, which will give you the character number (these numbers are specific to the dictionary. Then you can find the character inside the dictionary and read both its pronunciation and definition.

This is sometimes very easy, at other times very frustrating, especially when the character seems to be derived from more than one radical or when the shape of the radical is changed within the character (this is often the case because each character is drawn in the same size as any other character, hence the radical is often drawn "compressed").

Let I be an ideal in a commutative ring R. The radical of I is defined to be
rad(I) = { an : a is in I and n is a positive integer }.
Note that I lies inside its radical (take n=1). An ideal that equals its radical is called a radical ideal. A commutative ring is called reduced if the zero ideal is radical.

Lemma rad(I) is itself an ideal of R.

Proof: For if a,b are in rad(I) and r is in R then think about (a-b)m. Expand this using the binomial theorem and we get a linear combination of terms like arnm-r. As long as m is big enough either the power of a or the power of b will lie I. Hence, so does (a-b)m. Likewise (ar)m=amrm will lie in I for large enough m.

Examples In the ring of integers Z the ideal 20Z has radical 10Z. In general

rad(p1n1...ptntZ) = p1...ptZ
for distinct primes pi and positive integers ni.

A radical is the part of a Chinese character that often gives a clue to the character's meaning. For example, the word 湖 hu2, meaning lake, is built from another character 胡 pronounced hu2 that means beard , but it has a water radical 氵 on the left, meaning that the character sounds like hu2 but has a water-related meaning.

Radicals don't always convey meaning, sometimes they just differentiate a sound. For example, if you add the jade radical to 里 li3, which means mile, you get the word 理 "principle".

Radicals are used to help categorize characters for dictionaries. Characters will be grouped under the same radical, which narrows down the search. Experts differ on the exact number of radicals in Chinese, but 214 is a commonly used number.

You have to have some understanding of Chinese characters to find the radical and look up the word in a dictionary. Radicals may be written differently depending on where they are placed in the character. You also just have to know what to look for.

The radical of an integer n is defined as the product of the distinct prime numbers that divide n, without repetition. For example, since 8 = 23:

rad(8) = 2

Or, since 60 = 22 × 3 × 5, we have

rad(60) = 2 × 3 × 5 = 30

This definition is core to the abc conjecture, which states—in broad terms—that given three coprime integers a, b, c that satisfy a + b = c, there are only finitely many such triplets that satisfy

c > rad(abc)1 + ϵ

For any positive real number ϵ (Epsilon). In other words, the conjecture states broadly that c < rad(abc) with only finitely many exceptions, given the necessary conditions.

## See also

Galaxy SongAndy’s Brevity Quest 2019 () → Poincaré Conjecture

Rad"i*cal (?), a. [F., fr. L. radicalis having roots, fr. radix, -icis, a root. See Radix.]

1.

Of or pertaining to the root; proceeding directly from the root.

2.

Hence: Of or pertaining to the root or origin; reaching to the center, to the foundation to the ultimate sources to the principles, or the like: original; fundamental; thorough-going; unsparing; extreme; as, radical evils; radical reform; a radical party.

The most determined exertions of that authority, against them, only showed their radical independence. Burke.

3. Bot. (a)

Belonging to, or proceeding from, the root of a plant; as, radical tubers or hairs.

(b)

Proceeding from a rootlike stem, or one which does not rise above the ground; as, the radical leaves of the dandelion and the sidesaddle flower.

4. Philol.

Relating, or belonging, to the root, or ultimate source of derivation; as, a radical verbal form.

5. Math.

Of or pertaining to a radix or root; as, a radical quantity; a radical sign. See below.

Radical axis of two circles. Geom. See under Axis. -- Radical pitch, the pitch or tone with which the utterance of a syllable begins. Rush. -- Radical quantity Alg., a quantity to which the radical sign is prefixed; specifically, a quantity which is not a perfect power of the degree indicated by the radical sign; a surd. -- Radical sign Math., the sign &root; (originally the letter r, the initial of radix, root), placed before any quantity, denoting that its root is to be extracted; thus, &root;a, or &root;(a + b). To indicate any other than the square root, a corresponding figure is placed over the sign; thus &cuberoot;a, indicates the third or cube root of a. -- Radical stress Elocution, force of utterance falling on the initial part of a syllable or sound. -- Radical vessels Anat., minute vessels which originate in the substance of the tissues.

Syn. -- Primitive; original; natural; underived; fundamental; entire. -- Radical, Entire. These words are frequently employed as interchangeable in describing some marked alternation in the condition of things. There is, however, an obvious difference between them. A radical cure, reform, etc., is one which goes to the root of the thing in question; and it is entire, in the sense that, by affecting the root, it affects in a appropriate degree the entire body nourished by the root; but it may not be entire in the sense of making a change complete in its nature, as well as in its extent. Hence, we speak of a radical change; a radical improvement; radical differences of opinion; while an entire change, an entire improvement, an entire difference of opinion, might indicate more than was actually intended. A certain change may be both radical and entire, in every sense.

Rad"i*cal (?), n.

1. Philol. (a)

A primitive word; a radix, root, or simple, underived, uncompounded word; an etymon.

(b)

A primitive letter; a letter that belongs to the radix.

The words we at present make use of, and understand only by common agreement, assume a new air and life in the understanding, when you trace them to their radicals, where you find every word strongly stamped with nature; full of energy, meaning, character, painting, and poetry. Cleland.

2. Politics

One who advocates radical changes in government or social institutions, especially such changes as are intended to level class inequalities; -- opposed to conservative.

In politics they [the Independents] were, to use phrase of their own time. "Root-and-Branch men," or, to use the kindred phrase of our own, Radicals. Macaulay.

3. Chem. (a)

A characteristic, essential, and fundamental constituent of any compound; hence, sometimes, an atom.

As a general rule, the metallic atoms are basic radicals, while the nonmetallic atoms are acid radicals. J. P. Cooke.

(b) Specifically, a group of two or more atoms, not completely saturated, which are so linked that their union implies certain properties, and are conveniently regarded as playing the part of a single atom; a residue; -- called also a compound radical. Cf. Residue.

4. Alg.

A radical quantity. See under Radical, a.

An indicated root of a perfect power of the degree indicated is not a radical but a rational quantity under a radical form. Davies & Peck (Math. Dict. )

5. Anat.

A radical vessel. See under Radical, a.

© Webster 1913.

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