3,260 reputation
931
bio website lightandmatter.com
location
age
visits member for 2 years, 9 months
seen 2 days ago

I teach physics at Fullerton College, a community college in Southern California.


2d
asked 2.71828. And then another 1828.
Apr
17
awarded  Nice Question
Apr
5
revised Interpretation of Riemann rearrangement theorem
added 124 characters in body
Apr
5
asked Interpretation of Riemann rearrangement theorem
Mar
20
comment Ultrapower and hyperreals
related: mathoverflow.net/questions/88292/…
Mar
19
comment How do we decide which axioms are necessary?
I think we would like a number system to be (1) applicable to the real world and (2) convenient. There is no difference between the rationals and the reals with respect to #1, since real-world measurements have finite precision. However, it's very convenient to be able to have $\sqrt{2}$ and $\pi$ and call them numbers.
Mar
18
comment Probability [Sum of digits is even for a random number]
I guess there's an alternate form of this question that omits the restriction to 6-digit numbers. In that case, I think the answer is not well defined, because there is no notion of a uniform probability distribution on the natural numbers. For example, the numbers divisible by 3 can be put in a one-to-one correspondence with the numbers not divisible by 3, but that doesn't mean that the probability of getting a number divisible by 3 is 1/2. Nor is it 1/3.
Mar
7
awarded  Good Answer
Mar
7
awarded  Mortarboard
Mar
7
revised Do we need to formally teach the Greek Alphabet?
deleted 16 characters in body
Mar
7
revised Do we need to formally teach the Greek Alphabet?
added 409 characters in body
Mar
7
awarded  Nice Answer
Mar
7
revised Do we need to formally teach the Greek Alphabet?
edited body
Mar
6
answered Do we need to formally teach the Greek Alphabet?
Feb
23
answered Why is there antagonism towards extended real numbers?
Feb
22
comment LaTeX/TeX Vs. Mathematica for Typesetting
I don't even think of LaTeX and Mathematica as being in the same category. Mathematica is a computer algebra system. LaTeX is a typesetting system. I already own Mathematica...so will always have a copy of it This was not my experience. I bought a copy of Mathematica, and when I upgraded my Mac to a new version of MacOS, Mathematica stopped working. When I asked Wolfram how to get it working again, they told me I had to pay full price for a new copy of Mathematica.
Feb
13
awarded  Popular Question
Feb
11
comment Why are the rational numbers not continuous?
The question and all the answers so far are written in terms of point sets, which is fine -- that's the most common way of talking about this kind of things these days. But it's not the only way. Smooth Infinitesimal Analysis (SIA) has a completely different way of talking about what is meant by a continuum. Here's a pretty accessible treatment: arxiv.org/abs/0805.3307 In SIA, a curve is locally identical to a line, and lines and curves cannot be broken up into point sets.
Feb
11
comment Why are the rational numbers not continuous?
@keshlam: The reals can then be augmented further, creating the hyperreals, which are even more dense. What's special about the reals is not that they're in some sense maximally dense. There are denser systems. What's special about the reals is the completeness property.
Feb
9
comment How do you prove arc length is greater than chord length?
There is not going to be any generic answer to this question, because it depends completely on what set of axioms and definitions you're using. It's fairly common to define a line as a curve of extremal length, in which case the thing you want to prove is simply proved by pointing to the definition.