for exampleeis areal numberbutnot a rational number.

statements. ◮ These notes are not intended as a textbook. F F. Conjunction accords with the natural language use of the word “and”.

It is False if bothpandqare False. You might have been taught.

not both. T T

Related documents. ◮ 1 + 1 = 2

For example, in Linear Algebra, showing that a particular setis (or is not) a vector This is not an online course! MATH 36100: Real Analysis II Lecture Notes Created by: Dr. Amanda Harsy July 20, 2020 1.

How do we understand this decreasing and bounded below by 0. This isnotthe mathematical usage of “or”.

Have we proved that 1 = 0?No!We have not proven nbe a power series inxwith a radius, of convergenceρ > 0. converges to 0. 1. primitive statements (that is, logical variables) Real Analysis Semester 2, 2019 Partial Lecture Slides. Please sign in or register to post comments. If we definef: (−ρ, ρ)→Rby,f(x) :=. Show that the sequence (an:n∈N) defined by,an:=an/n!

conjunction ofpandqis the statement “2 + 5 = 7 and 1 + 1 = 0”. In your previous courses, you will have seen some simple proofs and constructed some You will need to take notes during the lectures. Inparticular it solves

yourselves. ◮ 2 + 3 = 7

In fact by the rigorous definition of convergence of series this sum isnot equal to any Rather they are an accompaniment to the lectures. However.

2 +.. a Consider the sequence (an:n∈N) defined by,an:= (2n−7)/(3n+ 2) for alln∈N. |x|n/|x 0 |n. You are expected to attend lectures. They are here for the use of anyone interested in such material.

subspace of a bigger vector space.

anything. Real Analysis Lecture ppt - Free download as PDF File (.pdf), Text File (.txt) or view presentation slides online. statement.

Contents ... Real Analysis I to help you with the concepts here.

Propositional logic

e= 2.

This is a collection of lecture notes I’ve used several times in the two-semester senior/graduate-level real analysis course at the University of Louisville. We want lead to ridiculous conclusions. 2. qis the statement “porq” and is denoted byp∨q.

First order logic.

nx the statement “2 + 5 = 7 or 1 + 1 = 2”. Ifpis the statement “2 + 5 = 7” andqis the statement “1 + 1 = 0”, thenp∨qis Find … This course has two main aims: Hint: show that “eventually” the sequence (an:n∈N) is monotonely M >0 such that|anxn 0 |< Mfor alln∈N∪{ 0 }.

◮ You will learn this rigorous definition and apply it in all sorts of contexts to ndiverges for allx 6 = 0 then we say that the, nis convergent for allx∈Rthen we say that. or thedeceptiveexpression

A precise notion of what constitutes a theorem.

A precise notion of what constitutes a mathematical proof. n Ifpis the statement “2 + 5 = 7” andqis the statement “1 + 1 = 2” then the

If 0< r <1 and|f(x)−f(y)| 6 r|x−y|

Ifpandqare statements, theconjunctionofp

Copyright © 2020 StudeerSnel B.V., Keizersgracht 424, 1016 GC Amsterdam, KVK: 56829787, BTW: NL852321363B01.

Such statements are called course.

Share. (the case|x|=ρdepends upon the particular power series). Therefore,|anxn| 6 M|x|n/|x 0 |n for 0 0. They are constructed from: This course is more about developing your skills in proof writing rather than about matter.

✷, n≡a You are expected to attend lectures. the statement “2 + 5 = 7 or 1 + 1 = 0”. By grouping one way we argue that the (infinite) sum is 0, while by grouping another

Don't show me this again. Making rigorous such precise properties of functions is also a central part of this

the important differential equation: Perhaps you can show this is true formally, butproving it rigorously is another

This involves starting with logicand the way it is used for alln∈N Please sign in or register to post comments. ◮ To study how to writemathematical proofs ◮ x> 2

To calculate lim 0 is convergent,{anx Ifpis the statement “2 + 5 = 7” andqis the statement “1 + 1 = 2”, thenp∨qis Please sign in or register to post comments. F T

If we have time, we may add some point-set 7.

Ifpis the statement “2 + 5 = 7” andqis the statement “1 + 1 = 0” then the p q p∧q


Some methods of proof. Letg: (0,∞)→Rbe the function defined by,g(x) := 12 (x+ 4/x). andqis the statement “pandq”, denotedp∧q. 2008/2009. n

Copyright © 2020 StudeerSnel B.V., Keizersgracht 424, 1016 GC Amsterdam, KVK: 56829787, BTW: NL852321363B01, Lecture notes, lectures Extra - theorem 5.5 - integrability and boundedness, Annotated Bibliography for Aboriginalities, Pessi - appunti completi diritto del lavoro.

Cauchy first did it in 1821, which in mathematics is recent history. To make this expression (and the other definition above) precise took a long time. Generally, we use upper case lettersA,B,C,.. .to denote compound

in mathematics. Theexclusiveuse of “or”: I will ride my bike or catch the train.

Real Analysis lecture ppt

We can combine statements to give new statements. 2. In the English language, there are two different usages of the word‘or’. ◮ This is not an online course! They are an ongoing project and are often updated. Without precision in reasoning it is easy to make (erroneous) arguments which ofe: This is probably the most important function in mathematics.

◮ You are expected also to utilise textbooks from the library (or elsewhere). (More on ‘rational vs real’ later.). 1.

Therefore this series converges and by the comparison test, nis absolutely convergent for|x|<|x 0 |.

The first is anapproximationwhile the later isnot even a precise alln∈N∪{ 0 }.

Welcome! ◮ potato You will need to take notes during the lectures.

Helpful? ◮ To studyReal Analysis, Consider as a motivating example, Euler’s numbere. 3.

It is True if one or both ofpandqare True.

MATHS332 Lecture Notes (all) ... Real Analysis (MATHS332) Academic year.

asq∨p; that is, conjunction and disjunction are commutative. 2. connectives

0 +a 1 x+a 2 x ◮ For allx∈Z,x 2 ≥ 0 thatfis a well-defined continuous function on(−ρ, ρ). Sometimes you will prove more general versions of the proofs from Real Analysis I.

This compilation has been made in accordance with the provisions of Part VB of the copyright act for teaching purposes at the University. both statements are true. Since. ◮ All maths lecturers are named TriThang.

n+.. there are three.

This used what is

Rather they are an accompaniment

The disjunction is aninclusiveuse of “or”, that is; it allows for the possibility that

way we argue it is 1.


to the lectures.

Ifpandqare statements, thedisjunctionofpand


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