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4 definitions
by
**ALPSMAC**

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.

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).

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).

by ALPSMAC
March 02, 2010

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.

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.

by alpsmac
February 23, 2010

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.

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.

The halting problem is not computable.

by alpsmac
February 23, 2010

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.

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!'.

Transcript show: 'Hello, world!'.

by ALPSMAC
March 02, 2010