A formally verified proof of the prime number theorem
... Recall that µ takes values {−1, 0, 1}, so we need to deal with integers too. Casting was an endless source of headaches. • We had parallel theories of primes and divisibility for ints and nats. • We had to develop properties of floor and ceiling functions. • We had to do annoying manipulations of mi ...
... Recall that µ takes values {−1, 0, 1}, so we need to deal with integers too. Casting was an endless source of headaches. • We had parallel theories of primes and divisibility for ints and nats. • We had to develop properties of floor and ceiling functions. • We had to do annoying manipulations of mi ...
Introduction to Proof in Analysis - 2016 Edition
... The golden rule when writing: never write anything whose meaning is unclear to yourself ! You can also use this text to find many detailed examples of how to write a proof correctly. The language of mathematics consists of assertions about mathematical objects. Mathematical objects include the natur ...
... The golden rule when writing: never write anything whose meaning is unclear to yourself ! You can also use this text to find many detailed examples of how to write a proof correctly. The language of mathematics consists of assertions about mathematical objects. Mathematical objects include the natur ...
A Triangular Journey
... pattern only and not across at the same time. These are the target group of students to move. Multiplicative students present will offer a different view. (b) A pattern students may report is as an extra person is added to the group so the number of total handshakes increases by 1 less than the numb ...
... pattern only and not across at the same time. These are the target group of students to move. Multiplicative students present will offer a different view. (b) A pattern students may report is as an extra person is added to the group so the number of total handshakes increases by 1 less than the numb ...
Infinity
Infinity (symbol: ∞) is an abstract concept describing something without any limit and is relevant in a number of fields, predominantly mathematics and physics.In mathematics, ""infinity"" is often treated as if it were a number (i.e., it counts or measures things: ""an infinite number of terms"") but it is not the same sort of number as natural or real numbers. In number systems incorporating infinitesimals, the reciprocal of an infinitesimal is an infinite number, i.e., a number greater than any real number; see 1/∞.Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. In the theory he developed, there are infinite sets of different sizes (called cardinalities). For example, the set of integers is countably infinite, while the infinite set of real numbers is uncountable.