prime

In traditional mathematics, an integer divisible only by 1 and itself.

Known to drive mathematicians mad searching for the next largest one - computers all over the world are continually searching. At the time of writing, the largest prime found was 12978189 digits in length.

1 is prime.
3 is prime.
7 is prime.

A joke in mathematical circles about the properties of induction goes something like:

Base case: 1 is prime
K+1 case: 3 is prime

Therefore all odd numbers are prime. QED

The joke being, of course - that due to faulty logic in the proof, the conclusion is that all odd numbers are prime - a clear fallacy (example: 21... 7*3=21 so 21 is NOT prime).

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computable

The property of a problem being solved by means of a Turing machine.

In other words, can we write a program to solve the problem? If so, then the problem is computable.

The sorting problem is computable. I can sort lists of things based on a common comparator.

The halting problem is not computable.

smalltalk

One of the most beautiful OO languages ever created. Runs in an image in a virtual machine and so, in some sense, has been running since its inception in the late 70s/early 80s.

Hands-down the most expressive OO language in existence - average internal method size as of 2007: 6.5-ish lines.

Best IDE: Cincom Smalltalk

Transcript show: 'Hello, world!'.

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set

The mathematical set is traditionally known as a collection of objects. It is one of the most general and useful structures in mathematics.

Z = the set of integer numbers... {...-1, 0, 1...}
R = the set of real numbers (all non-complex numbers)

Let Q be the set of people who understand this definition and let S be the set of people who care about this definition:

Q intersect S is simply Q.

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