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Apr
26
comment Probability theory without deductive closure
@ToddTrimble : "I am of the opinion that X, and cursed be they who say otherwise" really doesn't discourage anyone saying otherwise if they actually have something to say. $\qquad$
Apr
25
revised Probability theory without deductive closure
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Apr
25
comment Probability theory without deductive closure
@PaulTaylor : Thank you. I'd say cursed be those who can't use language. Someone down-voted this without saying why. I wonder what such people think they accomplish? Do they think their behavior discourages what they consider bad questions, even though they leave the poster with no idea what's bad about it and hence with no way of doing better? $\qquad$
Apr
24
asked Probability theory without deductive closure
Mar
14
revised explicit big linearly independent sets
Two small MathJax corrections.
Mar
10
awarded  Sportsmanship
Mar
10
comment Examples of common false beliefs in mathematics
@roysmith : Euclid didn't even consider $1$ to be a number. $\qquad$
Mar
10
comment Examples of common false beliefs in mathematics
@DavidRoberts : What he does for a living is that he makes a bundle off universal covers. $\qquad$
Mar
10
comment Examples of common false beliefs in mathematics
@NateEldredge : "Combinatorial Structure of the automorphism group of $S_6$" by T.Y. Lam and David B. Leep, Expositiones Mathematicae 11 (1993), no. 4, pp. 289--903. $$.$$ In this paper, it is claimed that the group of all $1440=6!\times 2$ automorphisms of $S_6$ has exactly three distinct subgroups of index 2, no two of which are isomorphic to each other. (One of those is of course the group of all $6!=720$ inner automorphisms.) $\qquad$
Mar
10
revised Examples of common false beliefs in mathematics
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Mar
9
comment Are there 'finitistic' nonrecursive functions (assuming Church's Thesis is false)?
A constructivist whose name I don't remember once told me the following example of what he claimed is a counterexample to Church's thesis: Measure how many inches of rain fall each day. The number of inches as a function of the day is a computable function (so he claimed) but (so he also claimed) is not recursive. $\qquad$
Mar
9
comment Are there 'finitistic' nonrecursive functions (assuming Church's Thesis is false)?
You shouldn't keep alternating in and out of MathJax within a single block of mathematical notation. I've cleaned that up and put in proper use of \text{} and made some other improvements in MathJax usage. Maybe if you look at them you can follow that example and get better results. In particular, writing {\ne} rather than just \ne can result in lack of proper spacing in some cases. In a number of instances you used {curly braces} in places where they had no effect at all on what got rendered, and that can complicate the task of editing. $\qquad$
Mar
9
revised Are there 'finitistic' nonrecursive functions (assuming Church's Thesis is false)?
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Mar
9
comment What are the most misleading alternate definitions in taught mathematics?
$\ldots\,$one has two different topologies, and the second one the two ends of the interval are glued together. This should convince the student that the way in which the manifold is connected together is a question of which sets are considered open. $\qquad$
Mar
9
comment What are the most misleading alternate definitions in taught mathematics?
I've always thought this same thing about the way in which topology is presented. Here's a simple example to help motivate the idea that the usual rigorous definition of a topology on a set captures the idea of the way a stretchable and bendable space is connected together: On the one hand, one could say the open subsets of the set $[0,1)$ are its intersections with open subsets of $\mathbb R$ with the usual topology; on the other hand one could allow sets containing $0$ to be considered open only if they include some subset of the form $[0,\varepsilon)\cup(1-\varepsilon,1)$. Then$\,\ldots$
Mar
9
revised What are the most misleading alternate definitions in taught mathematics?
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Feb
25
revised What are the most misleading alternate definitions in taught mathematics?
Obviously this needs to be the __square__ of the variance; otherwise it's not 4th-degree homogeneous.
Feb
24
revised What are the most misleading alternate definitions in taught mathematics?
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Feb
24
revised Convex combinations of Bernoulli Measures
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Feb
24
answered What are the most misleading alternate definitions in taught mathematics?