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1. viking says:

   April 28, 2009 at 4:28 am

   FIRST

   1 (one) is a number, numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of “unit length” is a line segment of length 1.

   Mathematically, 1 is

   * in arithmetic (algebra) and calculus, the natural number that follows 0 and precedes 2, the multiplicative identity of the integers, real numbers and complex numbers;
   * more generally, in abstract algebra, the multiplicative identity (“unity”), usually of a ring.

   For any number x:

   x·1 = 1·x = x (1 is the multiplicative identity)

   x/1 = x (see division)

   x1 = x, 1x = 1, and for nonzero x, x0 = 1 (see exponentiation)

   Using ordinary addition, we have 1 + 1 = 2.

   One cannot be used as the base of a positional numeral system; sometimes tallying is referred to as “base 1″, since only one mark (the tally) is needed, but this is not a positional notation.

   The logarithms base 1 are undefined, since the function 1x always equals 1 and so has no unique inverse.

   In the real number system, 1 can be represented in two ways as a recurring decimal: as 1.000… and as 0.999… (q.v.).

   Formalizations of the natural numbers have their own representations of 1:

   * in the Peano axioms, 1 is the successor of 0;
   * in Principia Mathematica, 1 is defined as the set of all singletons (sets with one element);
   * the Von Neumann representation of natural numbers, 1 is defined as the set {0}.

   In a multiplicative group or monoid, the identity element is sometimes denoted “1″, but “e” (from the German Einheit, unity) is more traditional. However, “1″ is especially common for the multiplicative identity of a ring, i.e. when an addition and “0″ are also present. When such a ring has characteristic n not equal to 0, the element called 1 has the property that n1 = 1n = 0 (where this 0 is the additive identity of the ring). Important examples are general fields.

   In Boolean algebra, 1 corresponds to true.

   One is its own factorial, and its own square and cube (and so on, as 1 × 1 × … × 1 = 1). One is the first figurate number of every kind, such as triangular number, pentagonal number and centered hexagonal number to name just a few.

   Because of the multiplicative identity, if f(x) is a multiplicative function, then f(1) must equal 1.

   It is also the first and second numbers in the Fibonacci sequence, and is the first number in many mathematical sequences. As a matter of convention, Sloane’s early Handbook of Integer Sequences added an initial 1 to any sequence that didn’t already have it, and considered these initial 1′s in its lexicographic ordering. Sloane’s later Encyclopedia of Integer Sequences and its Web counterpart, the On-Line Encyclopedia of Integer Sequences, ignore initial ones in their lexicographic ordering of sequences, because such initial ones often correspond to trivial cases.

   One is the empty product.

   One is the smallest positive odd integer.

   One is a harmonic divisor number.

   In computing, many programming languages and computer systems use 1 to represent the Boolean value true, but this is not as common as using 0 for false. The reverse also occurs.

   One is neither a prime number nor a composite number, but a unit, like -1 and, in the Gaussian integers, i and -i. The fundamental theorem of arithmetic guarantees unique factorization over the integers only up to units (e.g. 4 = 22 = (-1)4×123×22).

   One is the only positive integer divisible by exactly one positive integer (whereas prime numbers are divisible by exactly two positive integers, composite numbers are divisible by more than two positive integers, and zero is divisible by all positive integers). One was formerly considered prime by some mathematicians, using the definition that a prime is divisible only by one and itself. However, this complicates the fundamental theorem of arithmetic, so modern definitions exclude units. The last professional mathematician to publicly label 1 a prime number was Henri Lebesgue in 1899.

   One is one of three possible values of the Möbius function: it takes the value one for square-free integers with an even number of distinct prime factors.

   One is the only odd number in the range of Euler’s totient function φ(x), in the cases x = 1 and x = 2.

   One is the only 1-perfect number (see multiply perfect number).

   By definition, 1 is the magnitude or absolute value of a unit vector and a unit matrix (more usually called an identity matrix). Note that the term unit matrix is usually used to mean something quite different.

   One is the most common leading digit in many sets of data, a consequence of Benford’s law.

   The ancient Egyptians represented all fractions (with the exception of 2/3 and 3/4) in terms of sum of fractions with numerator 1 and distinct denominators. For example, \frac{2}{5} = \frac{1}{3} + \frac{1}{15}. Such representations are popularly known as Egyptian Fractions or Unit Fractions.

   The Generating Function which has all coefficients 1 is given by

   \frac{1}{1-x} = 1 + x + x^2 + x^3 + \cdots.

   This power series converges and has finite value if, and only if, | x | < 1

   Reply
   • scott says:

     April 28, 2009 at 4:54 am

     Can I have a cliff’s notes version of this “First”?!?

     Reply
     • IvanTheMildlyAnnoying says:

       April 28, 2009 at 6:21 am

       Yes. Here it is:

       FIRST!!!

       Reply
   • IvanTheMildlyAnnoying says:

     April 28, 2009 at 6:19 am

     You’ve been waiting a looong time to use that, haven’t you? *pat pat*

     Reply
2. IvanTheMildlyAnnoying says:

   April 28, 2009 at 6:20 am

   Actually, this was quite creative. Much better than the idiots who scream “FIRST!!!!ONE!!TWO!!!ELEBENTY!!!!” with no actual comment on the LOL.

   Reply
3. Centerfolds says:

   April 28, 2009 at 6:41 am

   I was gonna comment on the caption but now I feel like commenting on the first comment!

   Reply
4. DaffySaffy says:

   April 28, 2009 at 9:20 am

   Meh, he looks better in a wig and frock-coat as Mr Henry Fielding, co-founder of the Bow Street Runners. . .

   (“City of Vice”, currently re-running on E4 in the UK and Ireland)

   Reply
5. DragonRidingSorceress says:

   April 29, 2009 at 1:19 am

   This is made of Win!
   (Yes, so awesome, it needs its own capital.)

   Reply
6. Harpuia says:

   April 29, 2009 at 5:53 am

   No, it’s because they sound alike. I can’t spell rhyme, unless I just did, I don’t know.

   Reply
7. Vila Restal says:

   April 30, 2009 at 1:01 am

   The shame about poor old Ian McDiarmid is that he has the same problem as Alec Guinness, i.e. he’s bit in tons of stuff Radio plays, Theatre, Films and TV, but he shall be forever known as Emperor Palpatine. Here’s an example (I can’t remember what the radio play was) that I heard on Radio 7 one night roughly about 6:30pm – “And coming up next “whatever the play was called” being read by Ian McDiamid a.k.a Emperor Palpatine. ” Just goes to show that if you’re a great actor and play what could be refered to as an Iconic role, you’ll be forever known for it.

   Reply

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