User:Tsirel

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 * RETIRED

I am Boris Tsirelson, an experienced mathematician and less experienced wikipedian...

Articles I've written (started)
and also
 * Large deviations of Gaussian random functions
 * Standard probability space
 * "Non-Borel set" (now merged into Borel set)
 * Schroeder-Bernstein theorem for measurable spaces
 * Conditioning (probability)
 * Probabilistic proofs of non-probabilistic theorems
 * Unbounded operator
 * Equivalent definitions of mathematical structures
 * Catalog of articles in probability theory
 * List of types of sets

Articles I've contributed to

 * Probability space
 * Nonlocality
 * Wiener process
 * Local martingale
 * Central limit theorem
 * Baire set
 * Algebra over a field
 * Space (mathematics)
 * Absolute continuity
 * Fundamental lemma of calculus of variations

On different wikis (if you like)

 * Entanglement (physics) =
 * Theory (mathematics) =
 * Plane (geometry) =
 * Probability space =
 * Proof assistant =
 * Measurable space
 * Measure space
 * Standard Borel space
 * Measure algebra (measure theory)
 * Numerical calculations and rigorous mathematics
 * Examples and counterexamples in mathematics

Quantum mechanics is not a physical theory
"So, what is quantum mechanics? Even though it was discovered by physicists, it's not a physical theory in the same sense as electromagnetism or general relativity. In the usual "hierarchy of sciences" — with biology at the top, then chemistry, then physics, then math — quantum mechanics sits at a level between math and physics that I don't know a good name for."

- Scott Aaronson

About 0.999...
That is mathematics, of course. But it reminds me some physics. One often says that "99.9% of atoms is empty space", or "You are 99.999% Empty Space", or "99.9999999% of Your Body Is Empty Space", or "A hydrogen atom is about 99.9999999999996% empty space", and finally, "I will go further - it’s 100% space". Indeed, in physics we do not discover an infinite hierarchy of levels; rather, at some finite step we recognize that the "empty space", skipped so lightheartedly as containing "only" fields, was just the matter we are looking for. By the way, inside atom, a typical electric field strength is about 1012 V/m (volts per meter), and intensity (energy flux, irradiance) about 1020 W/m2 (watts per square metre), see here. Not at all empty space...

Oddities of mathematical terminology
A linguist would be shocked to learn that if a set is not closed this does not mean that it is open, or again that "E is dense in E" does not mean the same thing as "E is dense in itself".

A set, however, is not a door: it can be neither open or closed, and it can be both open and closed. (Examples?)

Like the alligator pear that is neither an alligator nor a pear and the biologist’s white ant that is neither white nor an ant, the probabilist’s random variable is neither random nor a variable. (Alligator pear = avocado; white ant = termite.)

"Finite measure" is a measure, but "signed measure", "vector measure" and "finitely additive measure" are (generally) not measures. On the other hand, every measure is both a signed measure and a finitely additive measure. That is, "signed" means here "not necessarily unsigned", "vector" means "not necessarily scalar", and "finitely additive" means "not necessarily countably additive". See also Measure (mathematics).

Unbounded operator on X means "not necessarily bounded operator, not necessarily defined on the whole X".

Dirac delta function is not a function; rather, it is a generalized function.

Constant random variable satisfies the definition of random variable even though it does not appear random in the everyday sense of the word.

Every differential equation is a stochastic differential equation but most stochastic differential equations are not differential equations.

In mathematics, a “red herring” need not, in general, be either red or a herring.


 * E ( P ( A | X ) ) = P ( A ). —


 * f ′ — f&amp;nbsp;′


 * ∈ ∉ ⊆ ⊇ ∅ ± ∞ &#8467;





Table of mathematical symbols

How_to_edit_a_page

∫ ∑ ∏ √ &minus; ± ∞ ≈ ∝ ≡ ≠ ≤ ≥ &times; · ÷ ∂ &prime; &Prime; ∇ ‰ ° ∴ ℵ ø ∈ ∉ ∩ ∪ ⊂ ⊃ ⊆ ⊇ ¬ ∧ ∨ ∃ ∀ ⇒ ⇐ ⇓ ⇑ ⇔ → ↓ ↑ ← ↔

&amp;int; &amp;sum; &amp;prod; &amp;radic; &amp;minus; &amp;plusmn; &amp;infin; &amp;asymp; &amp;prop; &amp;equiv; &amp;ne; &amp;le; &amp;ge; &amp;times; &amp;middot; &amp;divide; &amp;part; &amp;prime; &amp;Prime; &amp;nabla; &amp;permil; &amp;deg; &amp;there4; &amp;alefsym; &amp;oslash; &amp;isin; &amp;notin; &amp;cap; &amp;cup; &amp;sub; &amp;sup; &amp;sube; &amp;supe; &amp;not; &amp;and; &amp;or; &amp;exist; &amp;forall; &amp;rArr; &amp;lArr; &amp;dArr; &amp;uArr; &amp;hArr; &amp;rarr; &amp;darr; &amp;uarr; &amp;larr; &amp;harr;

Unicode character SCRIPT CAPITAL F (U+2131) can be typed as &amp;#x2131; — &#x2131;

Category:Mathematical formatting templates

cross out cross out

References 1
Template:Cite_book + Template:Cite_journal + Template:Rp +Template:Section link













References 2


















References 3










References 4

 * (1) $$a = 0$$

and have a label somewhere else ("equation (1)")




 * $$\frac{n(n + 1)}{2} + (n+1) = \frac{(n+1)((n+1) + 1)}{2}\,,$$

.

English
It's "a Euclidean" because it's pronounced "yoo-", not "oy-" like in German. Same reason for "a European" instead of "an European". But would still be "an Eulerian" though.

Usage of articles in math English
Should I write "if x and y are positive then a number z=x+y is positive" or rather, "if x and y are positive then the number z=x+y is positive"? On one hand, this z appears anew, it was not introduced before. On the other hand, given x and y, there exists only one z defined by that phrase. Boris Tsirelson (talk) 18:11, 12 October 2014 (UTC)


 * Using the lost grammatical adage "when in doubt, rephrase", I'd use "if x and y are positive then z=x+y is positive". But it forced to pick from one of the two choices I vote for the second one. --RDBury (talk) 18:57, 12 October 2014 (UTC)


 * Thank you. Yes, I feel forced to choose, since really I write more complicated texts :-) such as "...then the/a function f defined by...satisfies..." (and instead of "function" it could be a longer noun group, like "separable reflexive Banach space" etc). Or do you think I can always rephrase? How? Really, I also feel more comfortable writing "the", but I got unsure, being confused by opposite opinions, like this: but when you introduce me someone, you say "a friend of mine" even though he is uniquely defined, if not by your words then by your gestures. Boris Tsirelson (talk) 19:54, 12 October 2014 (UTC)


 * It may sound strange, but I don't mind if slightly different styles (as long as they are "correct") are used in a longer text. It can help avoiding monotonic repetition, of which there is plenty anyway in mathematical texts. But in the present case, the second option gets my vote too. YohanN7 (talk) 20:49, 12 October 2014 (UTC)


 * Thank you. Having vote 2:0 (or even 3:0, counting myself) I get more sure. No, I do not find it strange... I also like some variations; but I face this case quite often. But wait, do you say that these "a" and "the" are both correct, or not? Boris Tsirelson (talk) 20:57, 12 October 2014 (UTC)


 * I'm not a native English speaker (I'm Swedish), but I'd say, as a guess, that both options are correct, but the first option seems unusual, it doesn't seem to fit. Perhaps it would fit in a bigger example with more ingredients. YohanN7 (talk) 21:07, 12 October 2014 (UTC)
 * It depends a bit on how you "read it out loud inside your head" when reading. An equation like z = x+y can "be pronounced differently" when given a context. YohanN7 (talk) 21:17, 12 October 2014 (UTC)


 * The Language Reference Desk may be a better place to post this question. As a native English speaker I am sure that it should be the and not a, because as you said there exists only one z defined by that phrase. --catslash (talk) 23:18, 12 October 2014 (UTC)


 * Thank you; if you are sure, also I am. Yes, I understand it is a language question; but sometimes math jargon differs from usual English. Boris Tsirelson (talk) 05:57, 13 October 2014 (UTC)

Misc
MathJax update, thanks to Nageh.

Just to let you know, I have updated my mathJax user script to recent version 1.1 of MathJax. Notable change is the support for webfonts via CDN (i.e., no local font installation requirements). Details at the user script documentation page. Feedback welcome.

How to make SVG diagrams, thanks to Ryan Reich.

This question sometimes comes up and it bears answering as often as possible, since a lot of people have never heard that we should be using SVG, and of those who have, few seem to have an easy way of actually accomplishing it. This is addressed at Help:Displaying a formula, but their proposed solution relies on a somewhat arcane and arbitrary invocation of two different utilities, followed by a roundabout filtration through two major software packages, which is necessitated by one of them (pstoedit) requiring a costly proprietary plugin to work properly. And the end result is still unusable if your diagram has diagonal lines. Here's the right way:

pdflatex file.tex pdfcrop --clip file.pdf tmp.pdf pdf2svg tmp.pdf file.svg (rm tmp.pdf at the end)

Both pdfcrop and pdf2svg are small, free (if new and somewhat alpha) programs that work properly. I advocate pdflatex since with the alternative, you might be tempted to go the route of latex&rarr;dvips&rarr;pstopdf before vectorizing, and that runs into a problem with fonts that has to be corrected with one of the arcane invocations above. (There is a correct route, which is to replace that chain with dvipdfm, that I have never seen anyone suggest. Somehow, the existence of this useful one-step solution to getting PDFs from plain latex is always ignored.)

It has been road-tested on, most notably (for the complexity of its images) Triangulated category and found to work quite well.

I think for art like this it would be preferable to use .svg (a vector format) for the graphics instead of .jpg (a bitmap format), if possible. I use Adobe Illustrator for that but it's kind of expensive; the most popular free alternative seems to be Inkscape. —David Eppstein

"Editors making a challenge should have reason to believe the material is contentious, false, or otherwise inappropriate", according to When to cite.

Per WP:POV fork, "The generally accepted policy is that all facts and major points of view on a certain subject should be treated in one article. As Wikipedia does not view article forking as an acceptable solution to disagreements between contributors, such forks may be merged, or nominated for deletion."

Arbitration/Requests/Case/Monty_Hall_problem

Mathematics (use of sources)

11.4) If editors disagree on how to express a problem and/or solution in mathematics, citations to reliable published sources that both are directly related to the topic of the article and directly support the material as presented must be supplied by the editor(s) who wishes to include the material. Novel derivations, applications or conclusions that cannot be supported by sources are likely to constitute original research within the definition used by the English Wikipedia.

From WPM talk:

I think that the OR rule together with the Copyright law make coverage of mathematics (or any other subject) impossible. You have to think (commit 'original research') to do mathematics. The only alternative is to blindly copy from 'reliable' sources which violates copyright. Of course, such copying and the verification that the source is indeed reliable also require thought (OR). So the rule against OR is an absurdity which should be repealed. The reason we have a rule against OR is to try to avoid disputes about what is correct reasoning by appealing to an outside source. Notice that in mathematics, this is usually only necessary when one or more of the disputing parties is a crank or troll. However, refusing to allow an edit on grounds that it is OR is ultimately just an excuse for rejecting what we think is false without having to get the agreement of a crank or troll. JRSpriggs (talk) 03:05, 14 March 2011 (UTC)


 * This one is fairly complicated. I don't think it true that, outside of mathematics, OR and copyright makes coverage impossible.  The problem is that an allowable rephrasing in most fields becomes OR in mathematics, as even a change in notation does not fall in the "routine arithmetic calculation" exemption in Principles 11.