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1h
comment Non-Lipschitz homeomorphism from compact metric space to itself
You could've just made the inequality strict. $\;$
2h
comment Non-Lipschitz homeomorphism from compact metric space to itself
Sure. $\:$ Let $X$ be non-empty, and let $y$ equal $x$. $\;\;\;\;$
2d
comment Why Do The Axioms of Euclidean Geometry Not Need To Include the Definition of Space?
@timax : $\:$ Look at Tarski's axioms. $\;\;\;\;$
2d
comment optimal strategies for 2-player zero-sum games of perfect information
Note: $\:$ I have cross-posted this to MO. $\;\;\;\;$
Jan
23
comment Why Do The Axioms of Euclidean Geometry Not Need To Include the Definition of Space?
@timax : $\:$ That "problem" with Euclid's axioms would not be a lack of completeness, it would be them entailing too much, i.e., it would be that they aren't sound. $\;\;\;\;$
Jan
22
comment Why can a circle be described by an equation but not by a function?
On the other hand, we can define a function by $\;\;\; f(x)+(\hspace{.04 in}f(x))^{\hspace{.02 in}5} \: = \: x \;\;\;\;$. $\;\;\;\;\;\;\;\;\;$
Jan
21
revised optimal strategies for 2-player zero-sum games of perfect information
removed tag that I no longer think relevant
Jan
20
comment optimal strategies for 2-player zero-sum games of perfect information
From every state, the expected score for player A is +1, since A could win in at most three more moves. $\:$ Thus, if one broke ties by choosing the right-most of the tied states, then the play would go 0,2,3,2,3,2,3,..., which would make A only score zero. $\;\;\;\;$
Jan
20
comment optimal strategies for 2-player zero-sum games of perfect information
Note that "always make a move that maximizes your expected score, with ties broken arbitrarily" does not work. $\:$ One could have the deterministic game with states 0,1,2,3 all labeled A, 0 as the initial state and going to 2 as the only move from there, 1 and 3 as the moves from 2, 2 as the only move from 3, and winning as the only move from 1. $\;\;\;\;$
Jan
20
asked optimal strategies for 2-player zero-sum games of perfect information
Jan
14
comment Does a non-abelian semigroup without identity exist?
@Hayden : $\:$ Being cancellative on either side stops things like that. $\;\;\;\;$
Jan
12
accepted Can an orderable field always be ordered in a way that extends a given subfield's ordering?
Dec
26
awarded  Yearling
Dec
8
comment What is wrong with this proposed proof of the twin prime conjecture?
I want more spacing in the answer. $\;$
Dec
3
comment Matlab wrong cube root
Taking $-\sqrt[n]{-x}$ only works if you assume $x$ is negative. $\:$ "If you want to salvage what ... on the negative real axis is" not what's given in this answer, as can be seen from trying $\:z=8\;$. $\;\;\;$ You can actually "dodge this issue entirely by taking" $\:($ signum $(x))^n\cdot \sqrt[n]{|x|}\;$. $\;\;\;\;\;\;\;$
Nov
26
comment Proving the sum of the reciprocals squared converges
$S_n \: = \: 1+... \;\;\;$
Nov
26
comment The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
$\frac32 \: \in \: \{x\in R \: | \: x\geq 1\} \;\;\;$ but $\;\;\; \frac32 \not\in \mathbb{N}_1 \;\;\;\;\;\;\;$
Nov
26
comment The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
Is $R$ the ring of integers? $\;$
Nov
26
comment The function $G: x \mapsto 2^{x^2}$ maps $\mathbb{R}$ onto $\{ x \in \mathbb{R} : x \geq 1 \}$
Why is the codomain given as $\mathbb{N}_1$? $\;$
Nov
22
comment What is $\mathbb{F}_7[X]$?
The zero element of $\mathbb{Z}_7$ does not have a multiplicative inverse in $\mathbb{Z}_7$. $\;$