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Evgeny.Makarov
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Today,
06:33
evinda
replied to a thread
Check if N is composite
in
Number Theory
(Nod) Oh yes, that's what I meant. I wrote the time complexity when using the repeated squaring trick. I understand... (Smile)
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17 replies | 341 view(s)
Today,
05:18
Peter
replied to a thread
Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.10 (b) ...
in
Analysis
Thanks for the help, Euge ... I now have a way now to prove that 1 \gt 0 but I am concerned because it involves what Sohrab lists as a subsequent...
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3 replies | 54 view(s)
Yesterday,
05:06
Peter
started a thread
Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.10 (c) ...
in
Analysis
I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers...
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1 replies | 40 view(s)
Yesterday,
03:11
Peter
started a thread
Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.10 (b) ...
in
Analysis
I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers...
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3 replies | 54 view(s)
Yesterday,
02:51
Peter
replied to a thread
Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.12 ...
in
Analysis
I think I have made some progress with showing that \frac{a}{2} \gt 0 ... We have 2 \gt 0 (can we say this? How is this justified?) and so...
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1 replies | 28 view(s)
Yesterday,
00:25
Peter
replied to a thread
Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.10 (1) ...
in
Analysis
After a little reflection ... I have come to the following solution ... To show that a \in \mathbb{R} \ \{ 0 \} \Longrightarrow a^2 \gt 0 ......
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1 replies | 32 view(s)
Yesterday,
00:06
Peter
started a thread
Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.10 (1) ...
in
Analysis
I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers...
see more
1 replies | 32 view(s)
August 17th, 2017,
23:56
Peter
started a thread
Ordering on the Set of Real Numbers ... Sohrab, Exercise 2.1.12 ...
in
Analysis
I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers...
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1 replies | 28 view(s)
August 17th, 2017,
10:53
Evgeny.Makarov
replied to a thread
How do I merge two age groups per 10k from an abortion rate table?
in
Basic Probability and Statistics
Let us introduce some notations. Let age 12-17 be denoted by index 1 and age 18-19 by index 2. Let $a_i$ be the number of abortions and $r_i$ be...
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3 replies | 102 view(s)
August 17th, 2017,
06:05
Peter
replied to a thread
Limits of Sequences ... Stoll Theorem 2.2.6
in
Analysis
Thanks Opalg ... it gives me great confidence when you or Evgeny confirm my effort ... Thank you ... Peter
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3 replies | 60 view(s)
August 17th, 2017,
05:45
Peter
replied to a thread
Limits of Sequences ... Stoll Theorem 2.2.6
in
Analysis
After some reflection I have a proposed solution ... To show \text{lim}_{ n \rightarrow \infty } = 0 Now ... for any \epsilon \gt 0 the...
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3 replies | 60 view(s)
August 17th, 2017,
05:09
Peter
started a thread
Limits of Sequences ... Stoll Theorem 2.2.6
in
Analysis
In his book: Introduction to Real Analysis, Manfred Stoll does not prove parts (a) and (b) of Theorem 2.2.6 on the limits to certain special...
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3 replies | 60 view(s)
August 17th, 2017,
02:10
MarkFL
replied to a thread
231.12.3.65 Determine the smallest distance between a point and a line
in
Calculus
Small quibble...axis of symmetry is: t=-\frac{1}{105} So, since the parabola opens up, the vertex is a minimum, so the minimum distance will be...
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8 replies | 155 view(s)
August 17th, 2017,
00:59
MarkFL
replied to a thread
231.12.3.65 Determine the smallest distance between a point and a line
in
Calculus
For a parabola of the form: f(x)=ax^2+bx+c We know the axis of symmetry is at: x=-\frac{b}{2a} So, for:
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8 replies | 155 view(s)
August 16th, 2017,
21:58
MarkFL
replied to a thread
231.12.3.63 Determine the smallest distance between point and line
in
Calculus
Isn't this question a duplicate of the following? 231.12.3.65 Determine the smallest distance between a point and a line
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1 replies | 37 view(s)
August 16th, 2017,
03:25
Peter
replied to a thread
Open Sets - Unions and Intersections -
in
Analysis
Thanks for the critique ... and sorry for a couple of typos ... Really appreciate your feedback ... it is really helpful ... Peter
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8 replies | 129 view(s)
August 16th, 2017,
03:08
Peter
replied to a thread
Limits of Sequences ... Sohrab Exercise 2.2.7
in
Analysis
Hi Evgeny ... Well! Thank you for all the guidance and support ... not only with the logic of proofs ... but also with Latex ... I appreciate...
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3 replies | 68 view(s)
August 15th, 2017,
11:00
Evgeny.Makarov
replied to a thread
Limits of Sequences ... Sohrab Exercise 2.2.7
in
Analysis
To produce large left and right delimiters that correspond to the size of the formula inside, write \left before the left delimiter and \right before...
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3 replies | 68 view(s)
August 15th, 2017,
09:59
Evgeny.Makarov
replied to a thread
Open Sets - Unions and Intersections -
in
Analysis
This is a step backwards. First you should prove all reasonable properties of real numbers (such as the axioms of an ordered field and their...
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8 replies | 129 view(s)
August 15th, 2017,
05:40
Peter
started a thread
Limits of Sequences ... Sohrab Exercise 2.2.7
in
Analysis
I am reading Houshang H. Sohrab's book: "Basic Real Analysis" (Second Edition). I am focused on Chapter 2: Sequences and Series of Real Numbers...
see more
3 replies | 68 view(s)
August 14th, 2017,
22:25
Peter
replied to a thread
Open Sets - Unions and Intersections -
in
Analysis
Thanks Evgeny ... indeed! see your point! Nevertheless ...Will try a direct proof that \bigcap_{n=1}^\infty I_n is not open ... Step (1):...
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8 replies | 129 view(s)
August 14th, 2017,
13:19
Evgeny.Makarov
replied to a thread
Closed Sets - Sohrab Exercise 2.2.4 - Part 2
in
Analysis
We want to show that \ where $I_n=\left$. If $x\le0$, then $x\notin I_n$ for all $n$, so $x\notin\bigcup I_n$. Also, $x\notin(0,1)$. Similar for...
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3 replies | 85 view(s)
August 14th, 2017,
13:04
Evgeny.Makarov
replied to a thread
Open Sets - Unions and Intersections -
in
Analysis
Your proof that $\bigcap_{n=1}^\infty I_n=$ is correct. The interval $$ is not open because $0$ does not have a neighborhood that is contained...
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8 replies | 129 view(s)
August 14th, 2017,
01:14
Peter
replied to a thread
Open Sets - Unions and Intersections -
in
Analysis
Hmm ... just been pointed out to me (on the Physics Forums) that the intersection being closed doesn't mean it is not open ... Oh well ... back to...
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8 replies | 129 view(s)
August 14th, 2017,
01:09
MarkFL
replied to a thread
Solar Eclipse 2017
in
Chat Room
I was just reading about how tree leaves can form "pinhole cameras" and the eclipse can be seen in their shadows:
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4 replies | 162 view(s)
August 14th, 2017,
00:43
Peter
replied to a thread
Open Sets - Unions and Intersections -
in
Analysis
Try to show that \bigcap_{ n = 1}^{ \infty } I_n = where I_n = ( \frac{-1}{n}, 1 + \frac{1}{n} ) ... ... We need to show that ...
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8 replies | 129 view(s)
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August 18th, 2017
07:52 -
Evgeny.Makarov
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Re: How do I merge two age groups per 10k from an abortion rate table?
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However, I am not sure...
August 17th, 2017
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Re: How do I merge two age groups per 10k from an abortion rate table?
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Evgeny.Makarov
Let us introduce some...
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I like Serena
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Re: How do I merge two age groups per 10k from an abortion rate table?
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Evgeny.Makarov
Let us introduce some...
August 16th, 2017
03:03 -
Peter
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Re: Open Sets - Unions and Intersections -
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Evgeny.Makarov
For n \gt 0 where n \in...
August 15th, 2017
18:13 -
Peter
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Re: Limits of Sequences ... Sohrab Exercise 2.2.7
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Evgeny.Makarov
To show \text{lim } (...
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Opalg
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Re: Limits of Sequences ... Sohrab Exercise 2.2.7
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Evgeny.Makarov
To show \text{lim } (...
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Peter
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Re: Closed Sets - Sohrab Exercise 2.2.4 - Part 2
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Evgeny.Makarov
We want to show that \[...
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Peter
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Re: Closed Sets - Sohrab Exercise 2.2.4 - Part 2
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Evgeny.Makarov
For n = 1, the interval...
August 14th, 2017
21:28 -
Peter
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Re: Open Sets - Unions and Intersections -
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Evgeny.Makarov
Your proof that...
09:27 -
Ackbach
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Re: Closed Sets - Sohrab Exercise 2.2.4 - Part 2
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Evgeny.Makarov
For n = 1, the interval...
August 13th, 2017
20:10 -
Peter
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Re: Open Sets - Unions and Intersections -
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Evgeny.Makarov
After some reflection I...
August 8th, 2017
21:20 -
Peter
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Re: The AM-GM Inequality - Sohrab Proposition 2.1.25 ...
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Evgeny.Makarov
This is standard...
August 7th, 2017
14:30 -
lfdahl
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Re: true or false statement
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Another example is...
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Re: TiKZ Question on Plotting a Parabola
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The figure environment...
August 4th, 2017
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Peter
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Re: The Integers as an Ordered Integral Domain ... Bloch Theorem 1.4.6 ...
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If natural numbers are...
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Peter
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Re: The Integers as an Ordered Integral Domain ... Bloch Theorem 1.4.6 ...
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What exactly is the...
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Ackbach
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