# Tagged Questions

Parity is a mathematical term that describes the property of an integer's inclusion in one of two categories: even or odd. An integer is even if it is 'evenly divisible' by two and odd if it is not even. (Def: http://en.m.wikipedia.org/wiki/Parity_(mathematics))

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### The parity of the function $f(x)=x^{2^{x^2}}$?

Someone claims that $f(x)=x^{2^{x^2}}$ is an even function which I highly doubt. I claim that $f(-0.5)=(-0.5)^{\sqrt[4]{2}}$ which is an imaginary number and $f(0.5)$ is a real number. Can I have ...
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### The parity of the sum of a multiset (of integers) and of the cardinality of the odd submultiset are equal

This is a fairly simple concept, yet surprisingly difficult [for me] to state simply. Given a multiset of integers, $M$, of finite (but arbitrary) cardinality. And, $S_m$ is the sum over the ...
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### Is zero an even number? [duplicate]

A quick google returns the answer on the parity of zero: Zero is an even number. In other words, its parity—the quality of an integer being even or odd—is even. The simplest way to prove that zero is ...
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### Is this attempt of showing the square root of two is irrational valid?

Any odd integer squared is always odd, and likewise, any even integer squared is always even. Therefore, the square root of an odd number must be odd and the square root of an even number must be ...
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### Equal number of black and white neighbors in circle

There are $n\geq 12$ points on a circle, each colored black or white. When we consider the $5$ neighbors to the left of any point and $5$ to the right, then among the $10$ points, exactly $5$ are ...
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### Erasing numbers from circle and writing down sum

There are $50$ copies of the number $1$, and $50$ copies of the number $-1$, written alternately in a circle. In each step, we pick an arbitrary number, write down the sum of the number and its two ...
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### Generator matrix of a binary cyclic code

I need to find the Generator and Parity check matrix of a binary cyclic [9,2] code. If I calculated right, the Generator polynomial is x^7 + x^6 + x^4 + x^3 + x + 1 and the check polynomial is x^2 - x ...
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### Parity Bit Detecting Odd Bit Errors

I'm going over a past paper which has a true or false question with the following statement. A single parity bit computed over 128 data bits can detect an error when bit-flips occur in exactly 93 ...
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### Undetected Errors in 2 Dimensional Parity

Given a two dimensional parity with a data block of two rows and two columns what is the probability that a four bit error goes undetected? The naive method would be to look at all ways in which an ...