I'm honestly wondering what it's made of to go up in absolute flames like that?
That would be fine, I can live with choosing two of those for any given account.
What I hate is when the company offering the service forces its choice on me. I may be reliant on logging into some specific account without access to my phone, but then along comes company X and says "NOPE! Your account security is more important than you being able to access your own stuff. We're completely on board with locking you out of your own accounts in the name of security."
To be clear, I'm talking about personal accounts. Those on a network where I'm responsible for preventing a breach are another matter of course.
I'm surprised you're getting downvoted so heavily: Is it really that controversial of an opinion that I want to be able to make the choice between reliable accessibility, efficiency, and hardened security for my personal stuff?
Of course: On a corporate network I have a responsibility to have a very secure account so that I'm not a weak point, I'm not talking about scenarios where my account being breached exposes others that I'm responsible for.
I'm talking about my personal accounts. I may want to choose to have a password and no 2FA, for the simple reason that I may want to be able to access my account from a library computer or internet cafe without having access to any of my devices. That reliable access may be more important to me than having heavier security, and nobody has any business asking me why, because it's my data that I'm choosing how to protect. However, that's become pretty much an impossibility by now, with everyone shoving 2FA and whatnot down my throat, regardless of what I want.
If I happen to lose/break my laptop and phone simultaneously, which is not unthinkable given that I carry both on me pretty much every day, I'm pretty much locked out of everything.
Yes, there are an infinite number of velocities you can use, but if you look at their distribution, you'll find that it quickly goes to zero somewhere around 1-2 m/s, so the expectation value of the velocity is convergent.
If you have an object with a velocity taken from a distribution that doesn't approach zero sufficiently fast as the velocity goes to infinity, the expectation value diverges. A simple example would be a person that would be half as likely to get up at a velocity of 2 m/s as 1 m/s, and half as likely to get up at 4 m/s as 2 m/s, etc.
The more mathematical version of the same argument is to compute the kinetic energy of a particle whose wavefunction is a delta pulse (i.e. a particle whose position is exactly defined), and you'll find that the particle has infinite energy.
There are a lot of good answers here already, but I'll try to attack the question from a new angle.
Firstly, yes: they experience an attractive force from the nucleus, and would in principle have their lowest possible potential energy if they were located exactly in the nucleus. An equilibrium state is the state with lowest energy, so why aren't they exactly in the nucleus?
Consider that an electrons position and speed cannot be exactly defined at the same time (uncertainty principle). So an electron with an exact position could have any speed. If you compute the expectation value of a particles kinetic energy, when the particle can have any speed, you'll find that it's divergent (goes to infinity).
So: Because an electron with an exactly defined position must have infinite kinetic energy, the equilibrium state cannot be an electron with an exactly defined position, and so cannot be an electron exactly in the nucleus. So what do we do?
We have to make the electrons position "diffuse". Of course, that means it is no longer exactly inside the nucleus, so it gains some potential energy, but on the other hand it can move more slowly and has lower kinetic energy.
The equilibrium state is the state we find where the trade off between kinetic and potential energy gives us the lowest total energy, which is described as a 1s orbital. The electron is "diffuse" enough to have a relatively low kinetic energy, and "localised" enough to have a relatively low potential energy, giving as low total energy as possible.
Once you start adding more electrons you need to start taking Pauli exclusion into account, so I won't go there, but the same manner of thinking still essentially holds up.
Al lot of the same properties as a mine field. An unobserved mine field is quite quickly passed through. The issue primarily arises when you need to clear a mine field while under fire.
Combine them with ditches, barbed wire, possibly mines, and have forward observers directing fire on anyone trying to break through, and they're a real PITA for attacking forces.
Essentially, they give just a couple forward observers the power to hold up an attacking force for quite some time while reinforcements arrive, at which point you've lost whatever advantage of manpower or surprise you had when attacking.
While I get your point, I think it makes complete sense, and a big difference, when opinion pieces are labelled.
While I 100% agree with his reasoning, I hate to point out that the next governor might not care much about precedence.
To put this into perspective for all you Americans: In my country at least, we don't have "rallies" at all. It's not a thing. We have political debates and news broadcasts regularly where politicians from opposing parties are invited to speak their case, that's it. Of course, parties also have stands in public places where they give out pamphlets and promote their party, but in those places you'll likely find stands from a bunch of parties.
The way you do campaigning in the US is absurd to me.
I'm a person that regularly forgives people for "sins" committed in a time where what they were doing was considered normal by that time's standards but regressive by today's standards.
Honestly, it just feels refreshing to have a guy that's actually been pushing his ideals ahead of the status-quo and hasn't shirked from being "too radical".
I wouldn't go as far as calling it "mostly meaningless", but it definitely carries an enhancement bias, in that the better players will tend to be placed on the same team, where they mutually enhance each others goal/assist stats.
From a recruiting perspective for instance, I would assume that it would be interesting to devise a statistic to indicate how much a player improves the team they're on, while somehow factoring out the effects of the other players.
At the same time of course, a lot (most?) of what makes a good team is not just the skills of the individual players, but how the different players utilise each other's strengths and cover each other's weaknesses.
Holy shit! Does anyone have a location for this?