Cool Facts About Numbers

You probably work with numbers every day, sometimes without even realizing it. Did you know that even the first few numbers have something special behind them? Check out these cool facts about 0, 1, and 2.

0

is a separate and special entity called ‘Identity element’. 0 is actually the identity element under addition for the real numbers, since if a is any real number, a + 0 = 0 + a = a. Mathematicians refers to 0 as the additive identity (or better said, the reflexive identity of addition).

is considered to be a purely imaginary number: 0 is the only complex number which is both real and purely imaginary.

identifies the concept of “almost” impossible in probability. More generally, the concept of almost nowhere in measure theory.

0 = n / ∞

0 = loga1
a0 = 1, only when a doesn’t equal 0.

By convention, you cannot divide any number by zero.
In theory, zero multiplied by infinity is undetermined (as is zero divided by zero).

It is the only integer (actually, the only real number) that is neither negative nor positive. The question whether ‘zero’ is odd or even seems to be totally subjective!

 1

is a separate and special entity called ‘Unity’ or ‘Identity element’. 1 is actually the identity element under multiplication for the real numbers, since a x 1 = 1 x a = a. Mathematicians refers to 1 as the multiplicative identity (or better said, the reflexive identity of multiplication).

is NOT prime! Primes or prime numbers can be poetically described as the ‘atoms’ of mathematics – the building blocks of the world of numbers. But, mathematically speaking: “a prime number is a positive integer with exactly TWO positive divisors: 1 and itself”. Modern textbooks consider 1 neither prime nor composite, whereas older texts generally asserted the contrary. In 1859, Henri Lebesgue stated explicitly that 1 is prime in “Exercices d’analyse numérique”. It is also prime in “Primary Elements of Algebra for Common Schools and Academies” (1866) by Joseph Ray, and in “Standard Arithmetic” (1892) by William J. Milne. A list of primes to 10,006,721 published in 1914 by Derrick N. Lehmer includes 1 (“List of prime numbers from 1 to 10,006,721”, Carnegie Institution of Washington).

is the only real solution of the equation x3 + 3x – 4 = 0

 2

is the only even prime.
there are no integers x, y, and z for which xn + yn = zn is valid, when n is greater than 2

is the smallest prime that can grow 7 times by the right:
2 is prime,
29 is prime,
293 is prime,
2939 is prime,
29399 is prime,
293999 is prime,
2939999 is prime.
29399999 is prime.

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3 Comments.

  1. “The question whether ‘zero’ is odd or even seems to be totally subjective!”

    Really? How’s that? If by definition an odd number is one that leaves a remainder of 1 when divided by 2, and if 0/2 = 0 with no remainder, then 0 is surely not odd. On the other hand, an even number is one that leaves a remainder of 0 when divided by 2, it seems like 0 fits the bill for even numbers. Where is the “subjectivity”?

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    • William Lohrmann

      I agree. I don’t think I’ve seen one definition that suggests 0 should be odd. The subjectivity of it is probably just people getting confused :roll:

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  2. 🙁 👿 ❓ 😛 ❗ 🙂 😳 😀 😮 😮 😯 😕 😎 😡 😡 😈 😈 :roll: :roll: 💡 ➡ :mrgreen: :mrgreen: 😥 😐 😉

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