@BernardMeurer well, I did do schroedinger QM in first semester chemistry brag - but yeah, I'll agree with you, that's a lot to stomach right at the start :<
@BernardMeurer You don't "construct" $\pm\infty$. You just add two objects to $\mathbb{R}$ and call them $\infty$ and $-\infty$ and require that they fulfill $-\infty < x < \infty$ for all reals.
@0celo7 No, it doesn't, consider a function that oscillates infinitely often near $y$ while growing in amplitude. You wouldn't write $\lim = \infty$ for that, hopefully.
@BernardMeurer You don't need it to define that convergence, but using it (in particular the $-\infty < x < \infty$ part) saves you from always having to state the case $\lim = \pm\infty$ as an exception when writing down statements about limits (like $\forall n: a_n < b_n \implies \lim a_n \leq \lim b_n$).
I'm just trying to assure myself i'm not crazy. That is poor wording, isn't it? Shouldn't it be: "find the magnitude of the normal vector that extends to the origin?"
no i never got that far in d&f. stopped half way into group theory when things were getting hairy @0celo7
@0celo7 It's not wrong. But did you really think that when Obliv asked about what distance exactly is meant, he wanted to hear about normed vector spaces and affine spaces?
@heather actually i think ellipsoids and elliptic paraboloids are the only ones i think I can draw. it's the other ones that I'm going to have to improvise.
How is shor's algorithm implemented using quantum gates (in an ideal setting, I mean)? Even a reference that shows the diagram for this would be absolutely fabulous...
@heather I understood that part but I'm confused what he was expecting when purchasing a book on group theory. It's a mathematical theory in the first place.
@Obliv This was back when he wasn't a mathematician yet and had only heard of group theory in the context in which physicists use it, which is more representation theory and Lie theory to mathematicians.
@BernardMeurer dude I'd have to ship to the 3rd world
that would cost as much as the book
@ACuriousMind I really want to learn representation theory, and I'm debating whether to go right to Lie groups or go through finite groups first, which has profound geometric implications
@BernardMeurer Well, take electron degenerate gases for example. Two electrons (opposite spins) each occupy the energy states between the lowest possible energy and the Fermi energy.
When we're talking about electrons rising to new energy levels in that sense, are we saying energy is discrete?
For example, if two electrons occupy the same energy state, do they have the exact same energy? If they were to gain energy at all, would that necessarily put them in higher energy states?
Isn't there something about you not being able to differentiate between electrons at the same energy state? I don't know, I think it was in my chemistry notes
@DanielSank, I think I figured it out: 1. that is the matrix for 2 qubit quantum fourier transformations (and a Hadamard is the 1 qubit quantum fourier transformation) 2. A single qubit can be 0, 1, or a superposition of those two states ($\alpha |0\rangle + \beta |1\rangle$). Two qubits can be 00, 11, 01, 10, or a superposition of those four states, and so on. A quantum computer with $n$ qubits can be in a superposition of up to $2^n$ states at the same time.