# Theory of proveit.numbers¶

Covers all generic number concepts: sets of numbers (integers, reals, and complexes), number relations (<, $\leq$, >, $\geq$), and numeric operations (+, -, $\times$, /, mod, exp), and operations over numeric functions ($\sum$, $\prod$, $\partial$, $\nabla$, $\int$).

In [1]:
import proveit
%theory # toggles between interactive and static modes

### Local content of this theory

common expressions axioms theorems demonstrations

### Sub-theories

number_sets defining standard number sets: integers, reals, complexes, and important subsets of these rounding of real numbers, such as round, floor, and ceiling absolute value of reals (and subsets) and norm of complex numbers number representions: binary, decimal, hexidecimal adding numbers (repetitive counting) negating numbers (subtraction from zero) ordering relations of numbers: <, ≤ >, ≥ multiplying numbers (repetitive addition) dividing numbers (inverse of multiplication) divisibility operations such as x|y to indicate x is a factor of y modular arithmetic (i.e., remainders of division) exponentiating numbers (repetitive multiplication) logarithms (inverse of exponentiation) add function evaluation instances: ∑ multiply function evaluation instances: ∏ rates of change; calculus: ∂, ∇, etc. summation over infinitesimals, inverse of differentiation: ∫ complex- and real-valued functions of one or more variables

### All axioms contained within this theory

This theory contains no axioms directly.

#### proveit.numbers.division

This sub-theory contains no axioms.

#### proveit.numbers.logarithms

This sub-theory contains no axioms.

#### proveit.numbers.product

This sub-theory contains no axioms.

#### proveit.numbers.differentiation

This sub-theory contains no axioms.

#### proveit.numbers.integration

This sub-theory contains no axioms.