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11233
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location Hamilton, Canada
age 21
visits member for 2 years, 3 months
seen 15 hours ago

Engineering student at McMaster university who wants to learn math properly.


Jul
2
awarded  Curious
Jul
1
comment How can one prove that $\lim\limits_{\theta\to 0} \frac{\sin\theta}{\theta}=1$
@JohnJoy what's your definition of $\pi$ to start with? There are plenty that don't need to make any reference to trig functions whatsoever. They might assume facts that end up being logically equivalent to $\lim_{x\to 0} \sin x/x=1$, but I don't see how it's inevitably circular.
Jun
26
comment Do factorials really grow faster than exponential functions?
@Pacerier for a fixed $n$ that happens to be less than $a$, yes absolutely. But the point of the question (and answer) is in the behaviour of each function as $n$ grows arbitrarily large, and eventually a growing $n$ will always become bigger than any fixed $a$. So the question is meant to be read as "Why does $n!$ always eventually get (and stay) bigger than $a^n$ no matter what $a$ is?"
May
30
awarded  Nice Answer
May
29
comment How can Zeno's dichotomy paradox be disproved using mathematics?
@Hurkyl my understanding was that there isn't a significant difference to them. One says "he must always do something else first", the other says "he must always do something else before he passes". I know I wrote my sums in the backward order for this problem, but I only meant that for notational convenience.
May
29
answered How can Zeno's dichotomy paradox be disproved using mathematics?
May
16
comment How should I solve integrals of this type?
@JackM Differentiating $e^x\cos x$ or $e^x\sin x$ gives combinations of terms similar to your integrand. It stands that some combination of these might differentiate to give the integrand precisely; we then must figure out which combination.. You equate coefficients because you want to find the particular case where the (differentiated) functions are the same.
May
13
comment How to deduce whether $\sqrt{3}i \in \mathbb Q (u)$ or not, where u is a root of $x^3-2$
@Improve yes, with no extra effort. It's not a separate identical looking argument for the other roots or anything, you already have the entire result by that very statement you gave. Algebra can't tell the difference between the roots: it has no sense of 'where' they are, only the algebraic relationships they satisfy. So if it's not possible for one of them it can't be possible for any of them, because that would imply that algebraic relationships could somehow make a distinction between two quantities that satisfy all the same algebraic relationships, which is a contradictory statement.
May
12
answered How to deduce whether $\sqrt{3}i \in \mathbb Q (u)$ or not, where u is a root of $x^3-2$
May
3
comment What is a high rank tensor?
metric tensors are always $n\times n$, since they always take 2 vectors as input. The Riemann curvature tensor, which takes 4 inputs, might be closer to what you're looking for.
Apr
22
comment Why do folded concentric circles and rectangles form a hyperbolic paraboloid?
@KyleKanos Origami would tell you how to make it, not why it folds the way it does. The solution clearly lies in analyzing what internal forces and stresses in the paper are created by the folds and bending, which is pretty squarely in physics territory.
Apr
17
answered How to tell if points in $Z^2$ belong to a half-plane?
Apr
11
awarded  Yearling
Apr
11
answered $A \oplus C = B \oplus C$ but $A\neq B$
Apr
6
comment Sketch the graph of the polynomial function $P(x)= x(x-3)(x+2)$
Your intervals have their ends at each of the roots. These are $-2, 0,$ and $3$. So yes, $x=0$ should be included as a boundary and you should test on either side of it to figure out whether the polynomial is positive or negative there.
Apr
6
comment Calculus on manifolds
It's tedious in comparison. You can do it (by 'it' I mean set up an appropriate surface integral, not direct integration in $\mathbb{R}^3$ which doesn't work as Nicholas has pointed out), but you end up doing all the intrinsic calculations anyway. Adding other calculations and things to look out for on top of that doesn't make life easier in the long run.
Apr
6
answered Sketch the graph of the polynomial function $P(x)= x(x-3)(x+2)$
Mar
22
answered Intuitive idea of axiom of choice
Mar
18
comment Application of Composition of Functions: Real world examples?
A function is just a process that turns one thing into another thing. Anytime you're describing something that chains processes together one after the other you're composing functions. You find a probability distribution and then want to find its average. Find a particle's position as a function of time, and then its distance from its start point. Almost any time you want to do multiple things to a function you're composing it with other functions.
Mar
5
awarded  calculus