Limits and Infinite Series Lecture Notes for Math 226 by´Arpád Bényi
... Math 226 is a first introduction to formal arguments in mathematical analysis that is centered around the concept of limit. You have already encountered this concept in your calculus classes, but now you will see it treated from an abstract (and more rigorous) point of view. A main goal of this cours ...
... Math 226 is a first introduction to formal arguments in mathematical analysis that is centered around the concept of limit. You have already encountered this concept in your calculus classes, but now you will see it treated from an abstract (and more rigorous) point of view. A main goal of this cours ...
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... Qk , one is negative, one is positive, and all the others are nonreal. Then the zeros of Qk+1 , obtained by applying the functions `(x) and u(x) in (2) to the zeros of Qk , have the same distribution: one negative, one positive, and all others nonreal. Therefore, this distribution holds for every n ...
... Qk , one is negative, one is positive, and all the others are nonreal. Then the zeros of Qk+1 , obtained by applying the functions `(x) and u(x) in (2) to the zeros of Qk , have the same distribution: one negative, one positive, and all others nonreal. Therefore, this distribution holds for every n ...
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... one definition of mathematics is that it is “proving statements about abstract objects.” You probably first met this conception of mathematics in your secondary school geometry course. While Euclid wasn’t the first person to prove mathematical propositions, his treatment of geometry was the first sy ...
... one definition of mathematics is that it is “proving statements about abstract objects.” You probably first met this conception of mathematics in your secondary school geometry course. While Euclid wasn’t the first person to prove mathematical propositions, his treatment of geometry was the first sy ...
Ramsey Theory, Integer Partitions and a New Proof of the Erd˝os
... The original proof in [9] of ESL was based on establishing the recurrence relation f (n+1, n+1) ≤ f (n, n) + 2n − 1. By now, there are several proofs of ESL. In fact, Steele [27] has collected 7 of these proofs, and dubbed the following pigeonhole-type proof by Seidenberg [23] as “the slickest and m ...
... The original proof in [9] of ESL was based on establishing the recurrence relation f (n+1, n+1) ≤ f (n, n) + 2n − 1. By now, there are several proofs of ESL. In fact, Steele [27] has collected 7 of these proofs, and dubbed the following pigeonhole-type proof by Seidenberg [23] as “the slickest and m ...
Computability on the Real Numbers
... binary rational numbers Q2 := {z/2n | z ∈ Z, n ∈ N}. Computability concepts introduced via robust definitions are not sensitive to “inessential” modifications. It can be expected that they occur in many applications. On the other hand, computability concepts introduced via nonrobust definitions are ...
... binary rational numbers Q2 := {z/2n | z ∈ Z, n ∈ N}. Computability concepts introduced via robust definitions are not sensitive to “inessential” modifications. It can be expected that they occur in many applications. On the other hand, computability concepts introduced via nonrobust definitions are ...
On the expansions of a real number to several integer bases Yann
... Our last result is a metric statement concerning simple normality to distinct bases. Apparently, Hertling [16] was the first to establish the correct analogue of Theorem CS when normality is replaced by simple normality. Theorem H. Simple normality to base b implies simple normality to base b0 if an ...
... Our last result is a metric statement concerning simple normality to distinct bases. Apparently, Hertling [16] was the first to establish the correct analogue of Theorem CS when normality is replaced by simple normality. Theorem H. Simple normality to base b implies simple normality to base b0 if an ...
