34,266 reputation
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bio website blog.plover.com
location Philadelphia, USA
age
visits member for 2 years, 10 months
seen 1 hour ago

I am Mark Dominus, an amateur.

I have a blog that often carries articles about mathematics.

You can email me at mjd@plover.com.


4h
comment $\{ a + b\sqrt{2} \ : \ a, b \in \mathbb{Z} \}$ dense in $\mathbb{R}$?
Okay, I have posted that as an answer.
4h
answered $\{ a + b\sqrt{2} \ : \ a, b \in \mathbb{Z} \}$ dense in $\mathbb{R}$?
4h
comment $\{ a + b\sqrt{2} \ : \ a, b \in \mathbb{Z} \}$ dense in $\mathbb{R}$?
There may be a simpler way to go about it, but I believe it follows from For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $[0,1]$. The main argmuent used is the pigeonhole principle: Divide $[0,1]$ into $n$ subintervals; there are more than $n$ multiplies of $a$, so two must be in the same subinterval.
4h
revised What is the “fastest” increasing function that's useful in some area of math?
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4h
revised How to solve this horizontal multiplication $234\cdot 345\cdot 542 =?$
edited tags
5h
revised How to solve $234\times456\times542=$? multiplication mentally
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5h
reviewed Approve How to solve $234\times456\times542=$? multiplication mentally
12h
comment What are some interesting sole exceptions or counterexamples?
Related: Accidents of small $n$
15h
revised All variants of stars and bars / balls and bins problem
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17h
comment What are imaginary numbers?
@dustin Changing it does not add any clarity or correctness to the question, which was unnecessarily bumped to the front page.
20h
comment What are imaginary numbers?
@dustin Don't make gratuitious edits to old questions.
1d
revised Can anyone explain this quote about how mathematicians think?
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1d
revised Flattening quantification over relations
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1d
awarded  Enlightened
1d
revised Scores of six soccer matches
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1d
answered Scores of six soccer matches
1d
revised Scores of six soccer matches
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1d
awarded  Good Answer
2d
comment Prove that the set of points that make up the unit circle are uncountable
At your stage¸‘exhibiting’ means constructing an explicit one-to-one and onto function, with as much explanatory detail as is necessary to convince the grader that you understand exactly what the function is.
2d
comment Why can't a direct proof be made backwards?
I thought your idea was to show that $5x-2$ is odd (“$A$”) if and only if $x$ is odd (“$X$”), and $3x+1$ is even (“$B$”) if and only if $x$ is odd (“$X$”). Then you want to show $A\iff B$, and instead you show $A\iff X$ and $X\iff B$. Then $A\implies X$ (because $A\iff X$) and $X\implies B$ (bceause $X\iff B$), so $A\implies B$. And $B\implies X$ and $X\implies A$, so $B \implies A$.