910 karma · joined April 29, 2012
Possible reasons, off the top of my head:
1. Being approached by a recruiter or hiring manager and end up being given an offer you can't refuse (eg much more money, dream job, etc).
2. Your spouse or significant other has to move to another city for their job, you don't want to leave them, and your current employer won't let you work remotely.
2a. Ditto with needing to move to care for an older and/or ill family member.
3. A shift of passion into a new career.
4. Health problems that cause such an extended leave of absence that you may as well leave.
5. I've encountered some managers who are leery of people who have spent "too long" at one place, wondering, eg "Why did s/he stay there for ten years? Did this person just find a spot to coast and collect a paycheck? Why hasn't s/he moved on to bigger and better things?" I think this line of thinking is just as knee-jerk as being leery of "job hoppers".
I also watched my grandmother go through dementia in the last months before she passed away. It was hell.
Yes, and the poor would be wealthier if they had more money.
What is garbage like this article doing on HN?
If someone is in front of you banging on their keyboard, you need not have any assurance that they're doing work, either.
I guess in the latter case, the name would be Streetly or Streetr or something equally dumb.
So, denoting x = a + b sqrt(-5) in Z[sqrt(-5)], we define the norm[1] of x as follows:
N(x) = a^2 + 5b^2
Note that, in this case, N is a function from Z[sqrt(-5)] to the natural numbers.For x, y in Z[sqrt(-5)], it turns out that the following properties of the norm hold (proving them is fairly straightforward, as it's essentially "plug-and-chug" combined with a bit of reasoning about how things work in the natural numbers):
1. N(xy) = N(x)N(y)
2. N(x) = 0 if and only if x = 0
3. N(x) = 1 if and only if x = 1 or -1 (ie x is a unit).
So, if x is a nonzero nonunit that isn't irreducible, then we can, by definition, write x = y*z where y and z are also nonzero nonunits. Applying strong induction via the norm, we can show that x can be written as a product of irreducibles. Of course this product is, in general, not uniquely determined.
Your business has no right of any kind to exist. Period.
Isn't that how the "invisible hand" of the "free market" (or some such garbage) is supposed to work?
In particular,
2 * 2 = (-1 + sqrt(-3)) * (-1 - sqrt(-3))
gives two irreducible factorizations of 4 in Z[sqrt(-3)] (you can use norm arguments in Z[w] to show irreducibility). Note that the right hand side can also be written as (2w) * (2w^2)
however, since w is not in Z[sqrt(-3)], the two factorizations above are distinct in Z[sqrt(-3)]. They become the same factorization in Z[w].Edit: Another way to think about why Z[sqrt(-3)] doesn't have unique factorization is because it isn't integrally closed[1]--that is, there is a monic polynomial (ie a polynomial with a leading coefficient of 1) with coefficients in Z[sqrt(-3)] that doesn't have roots in Z[sqrt(-3)]. In particular, since w^2 + w + 1 == 0, w is a root of the polynomial x^2 + x + 1, which is monic over Z[sqrt(-3)]. It turns out that any unique factorization domain[2] is integrally closed. Since Z[sqrt(-3)] is not integrally closed, it is not a UFD.
[1]: https://en.wikipedia.org/wiki/Integrally_closed_domain
[2]: https://en.wikipedia.org/wiki/Unique_factorization_domain
Why should the penalty be reduced based upon InMobi's finances? If the fine bankrupts them, all the better!
Edit: Honestly, I don't know why companies can't be fined based upon a percentage of revenue taken over, say, the past year. A fine of 10% yearly revenue would actually make these bastards sit up and pay attention.
In an integral domain D, a nonzero element x is called irreducible if x is not a unit and whenever x = ab (for a, b in D), then one of a or b is a unit.
On the other hand, a nonunit element x in D is called prime if for all a, b in D, if x divides ab then x divides a or x divides b (by "x divides ab", I mean that there's some element--call it y--in D such that xy = ab).
In Z (or any unique factorization domain[1]), these concepts coincide. In Z[sqrt(-5)], however, there are irreducible elements that are not prime. In particular, 2 is irreducible in Z[sqrt(-5)], but it isn't prime, since 2 divides (1+sqrt(-5))*(1-sqrt(-5)), but 2 divides neither 1+sqrt(-5) nor 1-sqrt(-5).
[1]: https://en.wikipedia.org/wiki/Unique_factorization_domain
Good riddance.
"Fine. You want to try and force us to carry local French TV, and fully pay for the production of said local TV programs? We will be cutting off all Netflix access to France, effective immediately."
It would take less than ten minutes for these cowardly bureaucrats to cave.