The opposite of even.

All integers are either even or odd, with numbers evenly distributed (and alternating) across both sets. A test to see if an integer is even or odd is whether or not said number is cleanly divisible by two (if so, the number is even, otherwise it is odd). In an exponent-based number system, this test can be reduced to looking at the last digit, and determining whether it is cleanly divisible by two, with the same test applied.

A common programming construct is to perform a bitwise AND with a number and a single 1 bit, the boolean result of which will tell whether the number in question is odd:

`BOOL is_odd = test & 1;`

## How Odd...

Odd is a particularly Norwegian name for boys. It stands to reason that it is not much used in English-speaking countries, but even in Denmark and Sweden it is not much used. The name has very old roots, however. It was used in name combinations for both males and females, probably as a symbolic protection, as names back then were supposed to be strong and protective. To the old Norsemen the word meant spear or any pointy end, and in modern Norwegian it is still understood as the sharp end of something.

Names featuring Odd include: Jorodd (m), Oddbjørg (f), Oddbjørn (m), Oddborg (f), Oddfrid (f), Oddgeir (m), Oddgrim (m) Oddhild (f), Oddlaug (f), Oddleiv, Oddrun (f), Oddvar (m), Oddveig (f), Oddvin (m), Torodd (m)

Many old Odd combinations have been kept in use, but Odd has also become a name on its own, as well as part of numerous new combinations. From the 1920s to the 1940s the name featured in the top 5 lists of the most popular names given to boys, and although it's slightly rarer today, it is still a common name.

Famous Odd people include Odd Nerdrum, an eccentric painter who probably loves every funny bit of his name, Odd Børretzen, an author, poet and speaking singer whose thoughts are odd and delightful, and Odd Einar Dørum, leader of the Norwegian Left party and current minister of justice of the country.

Odd can be a pretty difficult name to have outside of Norway, unless you don't mind being odd, of course.

One man by that name who had moved to America at a young age found it quite insufferable after some time, and after hearing one joke too many he exploded: Enough laughs about my odd name! When I die, my headstone shall be blank - nobody shall joke about my name again!

Sooner rather than later, the man died and his friends rembered his words with deep regret. They buried him and placed a totally blank headstone at his grave.

But whenever anyone walked past it, they would look at the empty headstone and say: "Hmm, that's odd!"

A number (more specifically, an integer) is odd if it is not congruent to zero, modulo 2. In other words, when you divide the number by two, you will get some-number-and-a-half (not a whole number), or a number x is odd if (and only if) it can be written as x = 2n + 1 for some integer n.

If x and y are odd numbers, and z is an even number, then:

• x + y is even
• x * y is odd
• x + z is odd
• x * z is even

A function f is odd if for every value x in its domain, -x is also in the domain and f(-x) = -f(x). A graph of an odd function is symmetrical about the origin.

If f and g are odd functions, and h is an even function, then:

• nf(x) is odd for any real number n
• f(x) + g(x) is odd
• f(x) * g(x) is even
• f(x) * h(x) is odd
• f(g(x)) is odd
• f(h(x)) is even
• h(f(x)) is even
• If the domains of f and h overlap, then f(x) + h(x) is not even, but it is not odd either unless h(x) = 0

A polynomial of x is odd if the power of x in every term is an odd number. (Note that (-x)2n + 1 = (-x)*(-x)2n = (-1)*(x)*(x)2n = -((x)2n + 1); every term in an odd polynomial is an odd function.)

Odd polynomials are odd functions, and continuous odd functions can be approximated to any desired accuracy by odd polynomials. However, there are functions which are neither even nor odd, and there are polynomials which are neither even nor odd. This is different than for integers; every integer is either even or odd. (In fact, the function f(x) = 0 is both odd and even, thanks to ariels for setting this straight for me.)

BrianShader reminds me: You might like to point out that any function can be written as an even function plus an odd function.

It’s so odd how the lightning flashes

And so beautiful

Bring it now

Odd (?), a. [Compar. Odder (?); superl. Oddest.] [OE. odde, fr.Icel. oddi a tongue of land, a triangle, an odd number (from the third or odd angle, or point, of a triangle), orig., a point, tip; akin to Icel. oddr point, point of a weapon, Sw. udda odd, udd point, Dan. od, AS. ord, OHG. ort, G. ort place (cf. E. point, for change of meaning).]

1.

Not paired with another, or remaining over after a pairing; without a mate; unmatched; single; as, an odd shoe; an odd glove.

2.

Not divisible by 2 without a remainder; not capable of being evenly paired, one unit with another; as, 1, 3, 7, 9, 11, etc., are odd numbers.

I hope good luck lies in odd numbers. Shak.

3.

Left over after a definite round number has been taken or mentioned; indefinitely, but not greatly, exceeding a specified number; extra.

Sixteen hundred and odd years after the earth was made, it was destroyed in a deluge. T. Burnet.

There are yet missing of your company Some few odd lads that you remember not. Shak.

4.

Remaining over; unconnected; detached; fragmentary; hence, occasional; inconsiderable; as, odd jobs; odd minutes; odd trifles.

5.

Different from what is usual or common; unusual; singular; peculiar; unique; strange.

"An odd action." Shak. "An odd expression."

Thackeray.

The odd man, to perform all things perfectly, is, in my poor opinion, Joannes Sturmius. Ascham.

Patients have sometimes coveted odd things. Arbuthnot.

Locke's Essay would be a very odd book for a man to make himself master of, who would get a reputation by critical writings. Spectator.

Syn. -- Quaint; unmatched; singular; unusual; extraordinary; strange; queer; eccentric, whimsical; fantastical; droll; comical. See Quaint.

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