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course supplement - UCSD Math Department
course supplement - UCSD Math Department

... Finally, the real numbers allow one to compute the limit of sequences of rational numbers, such as n limn→∞ 1 + n1 = e. ...
Introduction to School Algebra [Draft] - Math Berkeley
Introduction to School Algebra [Draft] - Math Berkeley

On the Complexity of Resolution-based Proof Systems
On the Complexity of Resolution-based Proof Systems

Chapter X: Computational Complexity of Propositional Fuzzy Logics
Chapter X: Computational Complexity of Propositional Fuzzy Logics

The Closed Limit Point Compactness
The Closed Limit Point Compactness

Interactive Theorem Proving with Temporal Logic
Interactive Theorem Proving with Temporal Logic

A conjecture on composite terms in sequence generated
A conjecture on composite terms in sequence generated

... double Mersenne number then there are infinitely many composite double Mersenne numbers arising from generalized Catalan-Mersenne number sequences. Since every double Mersenne number is also a Mersenne number so that every composite double Mersenne number is also a composite Mersenne number. Then t ...
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doc

THE SEMANTICS OF MODAL PREDICATE LOGIC II. MODAL
THE SEMANTICS OF MODAL PREDICATE LOGIC II. MODAL

A Musician`s Guide to Prime Numbers
A Musician`s Guide to Prime Numbers

... correspond to a prime interval? Let us formulate some conjectures to motivate a more detailed analysis of the patterns we are noticing. Conjecture 1.1. Let S denote a starting tone and N = {4, 6, 8, 9, 10, 12}. Then the tones S + n for n ∈ N (in any octave) will never correspond to a prime interval. ...
An Introduction to Higher Mathematics
An Introduction to Higher Mathematics

Distribution of Prime Numbers 6CCM320A / CM320X
Distribution of Prime Numbers 6CCM320A / CM320X

Extracting Proofs from Tabled Proof Search
Extracting Proofs from Tabled Proof Search

The Project Gutenberg EBook of The Algebra of Logic, by Louis
The Project Gutenberg EBook of The Algebra of Logic, by Louis

Topological aspects of real-valued logic
Topological aspects of real-valued logic

Sample Segment
Sample Segment

Math 13 — An Introduction to Abstract Mathematics
Math 13 — An Introduction to Abstract Mathematics

... In elementary school you largely learn arithmetic and the basic notions of shape. This is the mathematics all of us need in order to function in the real world. If you don’t know the difference between 15,000 and 150,000, you probably shouldn’t try to buy a new car! For the vast majority of people, ...
C. Ordinal numbers
C. Ordinal numbers

P 5. #1.1 Proof. n N - Department of Mathematics
P 5. #1.1 Proof. n N - Department of Mathematics

SOME ASYMPTOTIC FORMULAS IN THE THEORY OF NUMBERS(`)
SOME ASYMPTOTIC FORMULAS IN THE THEORY OF NUMBERS(`)

McCallum ch 08
McCallum ch 08

... So the domain of f is the set of all values on the input axis for which there is a corresponding point on the graph. For example, Figure 8.1 shows the graph of k( x)  x  1, which we saw in Example 1(d) with domain x ≥ 1. The graph has no portion to the left of x = 1, starts at (1, 0), and has poin ...
Lecture notes on descriptional complexity and randomness
Lecture notes on descriptional complexity and randomness

15(3)
15(3)

Introduction to Logic
Introduction to Logic

Duality Theory for Interval Linear Programming Problems G. Ramesh and K. Ganesan
Duality Theory for Interval Linear Programming Problems G. Ramesh and K. Ganesan

... problems. Bector and Chandra [4] introduced a pair of linear primal-dual problems under fuzzy environment and established the duality relationship between them. Hsien-Chung Wu [12,13] introduced the concept of scalar product for closed intervals in the objective and inequality constraints of the pri ...
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Non-standard calculus

In mathematics, non-standard calculus is the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic.Calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the (ε, δ)-definition of limit starting in the 1870s. (See history of calculus.) For almost one hundred years thereafter, mathematicians like Richard Courant viewed infinitesimals as being naive and vague or meaningless.Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś. According to Jerome Keisler, ""Robinson solved a three hundred year old problem by giving a precise treatment of infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century.""
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