The set of integers is formed by combining the whole numbers with their negative opposites. This collection includes all positive counting numbers, zero, and the negative counting numbers, continuing infinitely in both directions as shown by the sequence: $$\dots, -3, -2, -1, 0, 1, 2, 3, \dots$$.

Integer

The branch of "pure" math that studies integers and integer-value functions

University of Michigan - Ann Arbor

Pure:
- Quantity (number theory)
- Space (geometry)
- Structure (Algebra)
- Change (mathematical analysis)
- Combinatorics
- Topology

Applied:
- Probability Theory
- Computational Science
- Mathematical Physics
- Operational Research

Focuses of Math

Wikipedia

A set that has additional features (e.g. operations, relations, metrics, topology)

Structure in math

Study of financial risk and uncertainty. Combines elements of Business, Data Science, Statistics, and CS to help quantify financial risk. Actuaries are mostly hired into the Financial or Insurance industries to model various economic uncertianties.

Actuarial Mathematics

Quantity (number theory)

Probability is the branch of math concerned with the likelihood of an event occuring, or the likelihood that an event is true. 

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