Reputation
Next privilege 15,000 Rep.
Protect questions
Badges
1 22 53
Newest
 Nice Answer
Impact
~197k people reached

2d
comment Comma placement inline math
@BrianO The first fragment can be read that way as well, imagine there's an implicit "where" or "with" after $f(x_j)$.
2d
comment Comma placement inline math
@BrianO I believe the OP is saying that you can read the sentence as "Given $f(x_j)$, where $j=1, ... N$, - our goal is to...". In this case the comma is clearly recommended.
Feb
10
answered Alternative Proof that $\sqrt{p}$ is Irrational when $p$ is Prime
Feb
10
answered Can sum of rationals be irrational?
Feb
10
comment Can an infinite sum of irrational numbers be rational?
And the linear independence of the terms follows from the transcendence of $\pi$, which is the cleverest part of the answer. In fact any power series with rational coefficients, evaluated at a transcendental value but having a rational sum, would have done. It makes me wonder if there are "super-transcendental" numbers, which are not roots of any power series with rational coefficients.
Feb
9
comment How limiting/ heavy is the “triangle inequality” assumption?
If you drop the triangle inequality, basically all you have left is a symmetric function from $X^2$ into the positive reals. The triangle inequality is responsible for every important property of a metric.
Feb
8
answered Why are the symbols of operations written on the left or right of the objects to which they apply?
Feb
8
comment Is it accurate to say that multiplication of two integers yields an integer?
@user7530 The important issue that needs to be dealt with here is that the OP thinks they can trust a computer's floating point circuits to tell them about math. This will just be over their head.
Feb
8
comment Is it accurate to say that multiplication of two integers yields an integer?
I just put $\sqrt 5^2$ into my computer and got $5.000000001$. Computers only do arithmetic approximately.
Feb
7
revised Intuitive meaning of the concept “computable”
added 204 characters in body
Feb
7
answered Intuitive meaning of the concept “computable”
Feb
6
comment Squaring both sides when units are different?
@TonyK But what does $\sqrt{9 \text{inches}}$ mean? You can't take the square root of an inch any more than you can take the square root of a tomato. The point I was making in my second comment is that your kinematics example has the units outside of the square root, because having them inside is meaningless.
Feb
6
comment Squaring both sides when units are different?
@TonyK But anyway, with that interpretation the statement in the OP isn't correct - it's not true that $\sqrt 9$ inches equals $\sqrt{0.25}$ yards.
Feb
6
comment Squaring both sides when units are different?
@TonyK Right, but $x$ here refers to the amount of inches, not the inches themselves, so it's still $\sqrt{2x}\ \text{inches}$, not $\sqrt{2(x\text { inches})}$.
Feb
6
comment Squaring both sides when units are different?
Are you sure it's not $9^{1/2}\text{inches}=0.25^{1/2}\text{yards}$? Because I don't know what it would mean to take the square root of of an actual physical inch.
Feb
5
comment Is there a solution for this problem ??
I think you have these wrong. First of all there's no number (other than 0) which increases by one when you put an extra digit in front of it. Second of all, conditions 1 and 3 together imply that the number must be 9876543210 (well, maybe 0123456789 if you allow leading zeros).
Feb
5
comment How did the rule of addition come to be and why does it give the correct answer when compared empirically?
It seems to me that the way you've phrased the question shows a little confusion. You ask "how" this "came to be", as if it's an arbitrary rule that someone had to invent. 25 + 19 is 44 because if you have 25 coins in one pocket and 19 in the other, then if you tally up the total you find you have 44. What you should be asking is, why is it that "carrying the one" always gives you the correct answer.
Feb
2
comment Law of Excluded Middle Controversy
At its heart, constructivism is about what it means for a mathematical object to exist. A materialist might already object that mathematical objects don't "exist" - they're just thoughts. At a stretch, you might say they exist because you can imagine them, that is, construct them. And now you come along with an object that not only is purely imaginary, but you can't even describe it or construct it in any way. What sort of "existence" is that? If I understand correctly, excluding the LEM makes non-constructive existence proofs impossible. Someone else will have to explain why.
Feb
2
comment Classification of homomorphisms $\mathbb Q \to \mathbb C^\times$
Does the situation change drastically if the injective condition is dropped?
Feb
2
asked Classification of homomorphisms $\mathbb Q \to \mathbb C^\times$