Subset

In mathematics, especially in set theory, a set A is a subset of a set B, or equivalently B is a superset of A, if A is "contained" inside B, that is, all elements of A are also elements of B. A and B may coincide. The relationship of one set being a subset of another is called inclusion or sometimes containment.

The subset relation defines a partial order on sets.

The algebra of subsets forms a Boolean algebra in which the subset relation is called inclusion.

Definitions

If A and B are sets and every element of A is also an element of B, then:

A is a subset of (or is included in) B, denoted by ,

B is a superset of (or includes) A, denoted by

If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B which is not an element of A), then

A is also a proper (or strict) subset of B; this is written as

B is a proper superset of A; this is written as

For any set S, the inclusion relation ⊆ is a partial order on the set of all subsets of S (the power set of S) defined by . We may also partially order by reverse set inclusion by defining .

Superset (disambiguation)

Superset may refer to:

Strength training

Strength training is a type of physical exercise specializing in the use of resistance to induce muscular contraction which builds the strength, anaerobic endurance, and size of skeletal muscles.

When properly performed, strength training can provide significant functional benefits and improvement in overall health and well-being, including increased bone, muscle, tendon and ligament strength and toughness, improved joint function, reduced potential for injury, increased bone density, increased metabolism, increased fitness, improved cardiac function, and improved lipoprotein lipid profiles, including elevated HDL ("good") cholesterol. Training commonly uses the technique of progressively increasing the force output of the muscle through incremental weight increases and uses a variety of exercises and types of equipment to target specific muscle groups. Strength training is primarily an anaerobic activity, although some proponents have adapted it to provide the benefits of aerobic exercise through circuit training.