Document
Document

Primitive Recursive Arithmetic and its Role in the Foundations of
Primitive Recursive Arithmetic and its Role in the Foundations of

Number Patterns (Sequences)
Number Patterns (Sequences)

Sets with a Negative Number of Elements
Sets with a Negative Number of Elements

Outline for Chapter 10
Outline for Chapter 10

... even suspected the existence of uncountable sets until Georg Cantor proved the following theorem, which can be used to show that many sets are uncountable. In particular we can use it to show that the set R of real numbers is uncountable. Theorem 4.1 (Cantor). Let A be a set. Then there is no surjec ...
Ackermann function
Ackermann function

Calculus 30 | Curve Sketching | Determining Extremes
Calculus 30 | Curve Sketching | Determining Extremes

Goldbach’s Pigeonhole
Goldbach’s Pigeonhole

2-1 Power & Radical Functions Extra Notes and
2-1 Power & Radical Functions Extra Notes and

R u t c o r Research Learning on finite metric spaces
R u t c o r Research Learning on finite metric spaces

06_lecture_20100202_Loops,_Random
06_lecture_20100202_Loops,_Random

... grouped to perform in sequence, like a program. The function is provided a name so that a new program can use the function. Functions are a foundation of “modularity” – when we’ve solved a problem, let’s allow it to be reused. If there’s a problem with the solution, we can fix the function without r ...
Accelerated Algebra 2 Semester 1 Pacing Guide
Accelerated Algebra 2 Semester 1 Pacing Guide

Chapter 2 - Essentials Guides
Chapter 2 - Essentials Guides

PPT 6.1 The Unit Circle
PPT 6.1 The Unit Circle

... sin  = 0. That will happen at 0 and multiples of  (or 180°). The domain then is all real numbers except multiples of . Since the range is: -1  sin   1, What is the range? sine will be fractions less than one. If you take their reciprocal you will get things greater than 1. The range then is al ...
2 k+1
2 k+1

Cardinality, countable and uncountable sets
Cardinality, countable and uncountable sets

2 k+1
2 k+1

5.4 Common and Natural Logarithmic Functions
5.4 Common and Natural Logarithmic Functions

The irrationality of pi by Anne Serban
The irrationality of pi by Anne Serban

Algebra-2-Pacing
Algebra-2-Pacing

end notes
end notes

Propositional Logic Syntax of Propositional Logic
Propositional Logic Syntax of Propositional Logic

Honors Algebra 2 A Semester Exam Review 2015–2016
Honors Algebra 2 A Semester Exam Review 2015–2016

Delta Function and the Poisson Summation Formula
Delta Function and the Poisson Summation Formula

Natural Deduction Calculus for Quantified Propositional Linear
Natural Deduction Calculus for Quantified Propositional Linear

History of the function concept

The mathematical concept of a function (and the name) emerged in the 17th century in connection with the development of the calculus; for example, the slope dy/dx of a graph at a point was regarded as a function of the x-coordinate of the point. Functions were not explicitly considered in antiquity, but some precursors of the concept can perhaps be seen in the work of medieval philosophers and mathematicians such as Oresme.Mathematicians of the 18th century typically regarded a function as being defined by an analytic expression. In the 19th century, the demands of the rigorous development of analysis by Weierstrass and others, the reformulation of geometry in terms of analysis, and the invention of set theory by Cantor, eventually led to the much more general modern concept of a function as a single-valued mapping from one set to another.