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Dec
19
comment Cutting a unit square into smaller squares
But seriously, not only would this be a pretty sadistic (and unrelated, considering the professor taught a course on rings and modules) homework question, it's Christmas break! How could I possibly have homework right now?
Dec
19
comment Cutting a unit square into smaller squares
My approach involves setting up a linear system of equations using the squares' side lengths and showing that the solution to this system must be unique. I didn't post details because (1) they're really long and (2) I didn't want to bias you guys towards a particular way of thinking about the problem.
Dec
19
awarded  Commentator
Dec
19
revised Cutting a unit square into smaller squares
added 112 characters in body; edited body
Dec
19
comment Cutting a unit square into smaller squares
You can "divide" or "cut" any way you can think of, but nowhere did I say you can "glue" :)
Dec
19
revised Cutting a unit square into smaller squares
deleted 3 characters in body; edited title
Dec
19
comment Cutting a unit square into smaller squares
Sorry, I didn't make it clear: it's not that the smaller squares add up to unit area, it's that you can literally assemble them into a unit square. To put it another way, you're only allowed to use scissors on the unit square, and every piece you're left with at the end must be a square.
Dec
19
asked Cutting a unit square into smaller squares
Dec
19
awarded  Nice Question
Dec
18
comment (Finitely) decimal expressible real numbers between [0,1] countable?
Definitely. What I meant is that no two finite representations refer to the same number.
Dec
18
awarded  Scholar
Dec
18
accepted Geometric argument that operators on $\mathbb{R}^3$ have an eigenvalue?
Dec
18
comment (Finitely) decimal expressible real numbers between [0,1] countable?
By the way, has anyone seen this set come up in another context?
Dec
18
comment (Finitely) decimal expressible real numbers between [0,1] countable?
Good point. Luckily, we don't have to worry about nonuniqueness when the decimal expansions are finite.
Dec
18
comment Geometric argument that operators on $\mathbb{R}^3$ have an eigenvalue?
Thanks, this is really nice! But you did cheat and use polynomials ;-)
Dec
18
revised Geometric argument that operators on $\mathbb{R}^3$ have an eigenvalue?
added 6 characters in body
Dec
18
comment Geometric argument that operators on $\mathbb{R}^3$ have an eigenvalue?
Yes, thank you.
Dec
18
comment (Finitely) decimal expressible real numbers between [0,1] countable?
Right. "333..." isn't a "legitimate" number, but "0.333..." is.
Dec
18
revised (Finitely) decimal expressible real numbers between [0,1] countable?
added 307 characters in body
Dec
18
awarded  Teacher