Mathematical Analysis

This definition extends to any collection of sets. A collection of sets is pairwise disjoint or mutually disjoint if, given any two sets in the collection, those two sets are disjoint.

Formally, let I be an index set, and for each i in I, let Ai be a set. Then the family of sets {Ai : i ∈ I} is pairwise disjoint if for any i and j in I with i ≠ j,

For example, the collection of sets { {1}, {2}, {3}, ... } is pairwise disjoint. If {Ai} is a pairwise disjoint collection (containing at least two sets), then clearly its intersection is empty:

However, the converse is not true: the intersection of the collection {{1, 2}, {2, 3}, {3, 1}} is empty, but the collection is not pairwise disjoint. In fact, there are no two disjoint sets in this collection.

A partition of a set X is any collection of non-empty subsets {Ai : i ∈ I} of X such that {Ai} are pairwise disjoint and
Sets that are not the same.

Calculus is the study of functions based on the premise that all smooth curves can be considered to consist of infinitesimally small straight segments (microsegments). One consequence of this premise is that arbitrary values on the generic microsegment are nilsquare (equal to zero when squared). This applies most obviously to the values of the microsegment around zero in y = x^2. Another consequence is that the applicable logic omits the law of excluded middle; that is, it would be false to say that an infinitesimal is either identical to or distinct from zero.

Thus for any smooth curve,

f'(x) = [f(x+E) - f(x)] / E

Where f'(x) indicates the rate of change of the function and where E (epsilon) is an infinitesimal microsegment. The process of working out rates of change is called Differentiation. The most useful form of the above equation is,

f(x + E) = f(x) +Ef'(x)

If the area beneath a curve between the origin and x is given by A(x) then,

A(x + E) = A(x) + EA'(x)

We also independently know that,

A(x + E) - A(x) = Ef(x) + 1/2f'(x)E.E

The second term on the RHS is the triangle beneath the microsegment and the first is the rectangle beneath that. Combining these equations, removing the null term, and cancelling E yields,

A'(x) = f(x)

This is the Fundamental Theorem of Calculus. It shows that the reverse differentiation of a function yields its area function. This process is called Integration. The name of the approach to calculus outlined here is Smooth Infinitesimal Analysis.

its a type of math that involves algebra and trigonometry.
The branch of mathematics that deals with limits and the differentiation and integration of functions of one or more variables.
Calculus is a math figure relating to targeting an object. Below is an example of calculus:

You are about to shoot a missile at plane. The plane is moving forward a little bit, so you aim in front of the plane so that the missile and plane collide.

NOTE: Calculus does not count as a mathematical figure if the "Missile" is Target-Locked. Calculus only counts if the "Missile" Is aiming ahead of the "Plane" to intercept. Target-Locking "Missiles" allways aim for the "Plane" and collide with it.