Coinductive Definitions and Real Numbers
Coinductive Definitions and Real Numbers

AN A-Z OF TRIGONOMETRY The unit circle is the curve in the plane
AN A-Z OF TRIGONOMETRY The unit circle is the curve in the plane

Caffeine in bloodstream (mg)
Caffeine in bloodstream (mg)

... original graph does not pass the horizontal line test. That is, for each output value (SA), there are two input values (r). Graphing the relation in part (e) shows a sideways parabola. It does not pass the vertical line test. That is, for each input (SA), there are two outputs (r). ...
CMSC 203 / 0202 Fall 2002
CMSC 203 / 0202 Fall 2002

Mathematical Logic
Mathematical Logic

Document
Document

AN INTRODUCTION TO LOGIC
AN INTRODUCTION TO LOGIC

Introduction to Matlab
Introduction to Matlab

1 LOGICAL CONSEQUENCE: A TURN IN STYLE KOSTA DO SEN
1 LOGICAL CONSEQUENCE: A TURN IN STYLE KOSTA DO SEN

... have the sentence ‘Every natural number has a successor’. On a rather abstract level of logic, one may envisage a deduction corresponding to the consequence relation in this example (the rule justifying this deduction is called the -rule), but syntactical consequence relations, unlike this one, usu ...
From: Jehle, G. and P. Reny, Advanced Microeconomic Theory, 2nd
From: Jehle, G. and P. Reny, Advanced Microeconomic Theory, 2nd

Chapter 2 Propositional Logic
Chapter 2 Propositional Logic

Functional Programming in R
Functional Programming in R

... No man ever steps in the same river twice, for it’s not the same river and he’s not the same man. Heraclitus Lisp, Haskell, F#, Clojure etc. Things are collections of fixed values which go through processes (functions) over time ...
Day 11 - May 11, 2002 - Angelo State University
Day 11 - May 11, 2002 - Angelo State University

X - UOW
X - UOW

Combining Paraconsistent Logic with Argumentation
Combining Paraconsistent Logic with Argumentation

QUASI-MINIMAL DEGREES FOR DEGREE SPECTRA 1
QUASI-MINIMAL DEGREES FOR DEGREE SPECTRA 1

Proof theory of witnessed G¨odel logic: a
Proof theory of witnessed G¨odel logic: a

Relevant deduction
Relevant deduction

Expressiveness of Logic Programs under the General Stable Model
Expressiveness of Logic Programs under the General Stable Model

Beyond Quantifier-Free Interpolation in Extensions of Presburger
Beyond Quantifier-Free Interpolation in Extensions of Presburger

Foundations of Computation - Department of Mathematics and
Foundations of Computation - Department of Mathematics and

(pdf)
(pdf)

Common Core State Standards Supplement, SE
Common Core State Standards Supplement, SE

Distribution of the zeros of the Riemann Zeta function
Distribution of the zeros of the Riemann Zeta function

Logic and Mathematical Reasoning
Logic and Mathematical Reasoning

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.