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''' Did you know?   A few hack, cracks and obfuscated examples, which may actually lead to less confusion and a greater knowledge of why things work and how. However, these examples have a purpose, and should not be taken, in any way as correct or just another way to achieve a common goal. They are purposely, in some cases, convoluted.   I. String, things, hacking, and... read more

Blogs

Containment and Equality If A and B are sets, then A is said to be contained in B iff (if and only if) every element of A is contained in B. So A⊆B means that A is a subset of B. Example: All squares ⊆ all rectangles All right triangles ⊆ all triangles Important! This implies the idea of forwards and backwards logic: If Joe has three million dollars, he is a millionaire... read more

Blogs

Sets and Other Elementary Subjects Sets are a collection of things called objects. Objects are all unambiguously defined. In other words, objects have unmistakably clear definitions with one meaning and one interpretation that leads to one conclusion. This may seem convoluted because we are so used to words and phrases having different meanings and whatnot, but not in this case. Look... read more

Lessons

Sets A set is one of the most fundamental concepts in mathematics. Sets can be taught at an elementary level all the way through higher level mathematics. A set is defined as a group or collection of distinct objects. The elements of a set can be anything: numbers, people, letters, etc. The way we usual denote sets is by giving them capital letters for a name. Given set A and B A... read more