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Jun
27
answered Ways to study mathematics while commuting
Jun
27
comment Topologies on n-manifolds
Do you mean other topologies? Or other topologies on $n$-manifolds? If the former then you'll find you need to understand the compact-open topology if you intend to study homotopy theory. en.wikipedia.org/wiki/Compact-open_topology
Jun
25
comment Where does this unit vector come from?
There is a sphere here :-) The reason is that unit vectors are vectors of length 1, i.e. if you place the vector's tail at the origin its head lies on the unit sphere. So, in disguise, your question is "where does the vector $F_1$ meet a unit sphere?"
Jun
25
comment Is this mathematically correct?
Well $v_1/v_2=13/15$ but $r_1/r_2=1$ for row 1. But suppose there are errors up to 10% in your voltage measurements, so, eg. $v_1$ is actually 2.8 and $v_2$ is actually 2.8, etc., then the relationship might hold exactly.
Jun
25
comment Is this mathematically correct?
The relationship doesn't hold exactly. But if your voltage measurements are only accurate to 0.5V, say, then it is possible that the relationship holds. That's why experimenters give error bars when they publish results. Do you have some estimates of your uncertainty?
Jun
25
revised Convergence of two power series
Type in title
Jun
25
suggested approved edit on Convergence of two power series
Jun
25
answered Complex analysis is more “real” than real analysis
Jun
24
comment What should I learn first, Mathematica or MatLab?
Want to define a function? Stick an underscore after the argument names. Want to apply a function to some arguments? Use square brackets. Want to get the $i$th element of an array, use double square brackets. While one might quibble about what is or isn't natural, saying my claim that Mathematica notation "can look very unnatural" is outrageous is, well, interesting.
Jun
24
comment How to establish this inequality without using induction?
Seeing as you defined the $a_n$ by induction it's going to be completely impossible to prove any non-trivial property of them without using induction in some form or other. Maybe you're trying to rule out one particular induction proof.
Jun
22
comment logic\math question
If you look at the following link you'll see a number of examples that fit the pattern, some of which suggest answers other than 90: oeis.org/…
Jun
20
comment Writing a chain of implications in English
@porton I see your point and I like your emphasis on clarity. But an expert mathematician will realize that an empty set of propositions contains none that fail to follow. And a non-expert mathematician won't even notice that there is an issue. So I'm not sure who, in reality, would have a problem.
Jun
20
comment Writing a chain of implications in English
It seems clear to me. Maybe it's worth saying "Each of these four assertions..." just in case readers are tempted to include the following paragraphs.
Jun
20
comment Writing a chain of implications in English
Each of these assertions implies the following ones.
Jun
20
answered Neighbourhood of a matrix
Jun
20
comment Using dimensional analysis to evaluate $\frac{d}{dx}x^n$
You don't need to prove everything from scratch. When students first compute derivatives of monomials they often do the product rule first so they know monomials will have derivatives before they compute them. As for not appealing to heuristics, my entire PhD was based on using heuristics from physics to prove mathematical results, once they were appropriately formalised. Dimensional analysis is completely formalisable in mathematics.
Jun
20
comment Category-theoretic description of the real numbers
Also maths.mq.edu.au/~street/EffR.pdf
Jun
19
revised Smooth transition between two quaternions?
Incorrect spelling
Jun
19
suggested approved edit on Smooth transition between two quaternions?
Jun
19
comment Category-theoretic description of the real numbers
I don't know much about toposes. But curiously the people who've written about this construction seem to work with toposes a lot. I feel like in some sense this construction gets to the very heart of what real numbers are about. It seems like a generalization of reasonable (in some sense) strategies for sharing $M$ objects between $N$ people. I haven't worked out the details of that yet though...