I guess i might be answering my own question here, but is it because of how we chose to represent our functions? That is, for the lack of better term, strech it along the x axis? Has it it been f(y) would it be the other way around?
I know that it is defined such that there is no more than one y-value output for any given x-value input, but I"m wondering WHY it is defined that way? Why can't we apply everything we know about functions to equations that have more than one y-value output for any given x-value input?   In short, what is the benefit or reason to define a function this way?  At the same time, a little historical context would also be appreciated (i.e., when the concept originated and why).  Thanks,  Moshe
Travelling to Italy without my spouse who is a UK citizen I am India citizen married to a UK national who has been issued a Schengen Visa from the Italian consulate as a spouse of a UK national. My husband was supposed to travel with me but now can’t. We have decided that I should still pursue the trip without him as I will be joining our friends there. Please can someone let me know if I will still be allowed to travel to the Schengen region with a valid Schengen Visa issued as a spouse of a EEA national but without my husband joining me there in person ? Arbitrary precision spline interpolation Tikz, Tree without overlaps What is a word that means "someone who pretends to be your friend but is actually your enemy?" What do you call someone who pretends to be your friend but is actually your enemy?  A friend suggested spy for me, but that does not nearly describe the word I need for an English project. The character is very good at manipulating how people see him. He's a good liar. And pretends to be your friend but actually is your enemy. Let $P(x)$ be a degree $n$ polynomial with distinct roots $r_1, r_2, \cdots r_n$. Prove that   $$\displaystyle\sum_{i=1}^{n}\frac{P''(r_i)}{P'(r_i)}=0$$  My proof: We can equivalently rewrite the polynomial as $(x-r_1)(x-r_2)\cdots(x-r_n)$ and if we plug in the roots in the polynomial, we get that all of them are equal to $0$ so their first derivatives are equal to $1$ and then their second derivatives are equal to $0$ which means that all quotients are equal to $0$ and there for the sum is as well, $Q.E.D$  Don't show the solution please, but if you have a hint, feel free. Thank you. I've lost a command block, how can I find it? I've placed a command block making it day all the time. I want to turn it off, but I've lost it. What's the quickest way to find it? There's something funky about some titles in revision histories here on Meta Stack Exchange Quantum mechanics textbooks that use path integrals I'm looking for a textbook in quantum mechanics that relies heavily on Green functions and the path integral formalism to supplement my QM books. I want to do some calculations using alternative methods (path integrals, green functions, Lagrangians etc). I am trying to calculate the last two digits of $3^{400}$, but working $\bmod {100}$ is proving intractable. I did the last digit case pretty handily, and now I'm stuck at last two. How safely bring lamp wire into house? I'm considering replacing an outdoor lighting fixture with an LED motion-sensitive fixture, but I'm not sure how to safely do the wiring.  The location is protected (under a porch) but still needs to be weatherproof. Here's the existing fixture and mount:    The obvious replacement would be another lamp that included its own box cover, so that its wiring would be covered and protected. But, the fixture I like doesn't include such a cover:    You can see it's meant to be screwed into the wall, but doesn't cover anything. The power cable ends with bare wires which are meant to be wire-nutted to the supply wiring, probably inside a junction box. But, how do I get the wire safely into the junction box while keeping things weatherproof?  One option would be to replace the lamp's power cable with one ending in a grounded plug, and install a weatherproof outlet box. But that's ugly and complex.  Are there weatherproof junction box covers that include provisions for sealed entry of cables? Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$ Fast Pixel Search in Java How to jump to the region header from the endregion tag in c# visual studio 2012? How to get Ubuntu download for a Mac? Adding other css files to wp_head Windows 10 64-bit requirements: Does my CPU support CMPXCHG16b, PrefetchW and LAHF/SAHF? I'm currently trying to find out whether or not it would be a good idea to update my slightly dated notebook (Windows 7, 64-bit) to Windows 10. The problem is that Microsoft states in their  that to use the 64-bit version of Windows 10, a processor which supports CMPXCHG16b, PrefetchW and LAHF/SAHF is needed. I know that my processor is 64-bit (Intel Core i5-2430M @ 2.40 GHz) but I don't know how to find out whether it supports CMPXCHG16b, PrefetchW and LAHF/SAHF, and I have no idea what these mean.  I tried using Google and got no results that made sense to me, only some comparison of my i5 and a similar AMD processor. I also checked Intel's ARK website. If somebody could point me to where I can get more info I would be really grateful. How diodes protect H-bridge DC motor driver? I don't really understand how these diodes in this circuit and similar circuits (like driving a relay circuit) protects the controller circuit from the energy stored by the inductance of the coil. I really appreciate if someone could graphically explain it. ( I mean how the the diodes block the current and etc)  the second question about this circuit is the capacitor. what happens if it isn't there? Is it ever a good idea to close credit cards? I have a bunch of credit cards with no balance, while others have fairly high balances. I'd like to close the 0 balance cards, but I know that will reduce my overall balance and hurt my credit rating, since my ratios of used to unused credit will rise.  Is it ever a good idea to close credit cards? Can I safely use my camera with a external power supply? Top of answer covered by sticky top bar after clicking direct link With the introduction of the network-wide sticky top bar , I noticed a bug that's happening on every site (except for Stack Overflow). When you click on an answer link (of the form https://site.stackexchange.com/a/####), the very top of the answer and the upvote button are covered by the top bar:    Stack Overflow shows the correct behavior: