Thanks, I was thinking the same. I had already wrote a proof that worked if all a_i are defined like that, but wanted to be sure.
cosecantphi
They have surrendered, and they have not surrendered, they are defeated, and they are undefeated. Truly, Iran is a land of contrasts.
I'd hope neither exist 100 years from now
I don't think he meant to imply people working those jobs are lesser in anyway nor that that we don't need janitors and restaurant workers, just that working these jobs sucks in most cases, you will be abused by your employer and often thrown away like trash when they are done with you, and in most cases they do not pay a living wage.
The great thing about settlers is that so many of them have somewhere else to realistically go, which means they will be losing a very significant fraction of their population fleeing the war. I can't see how that won't cause serious destabilization internally.
What I wouldn't do for a history book written a hundred years from now...
What does that mean, how can he be excused from military service if the military is already volunteer only?
Either that or it tries to gaslight you into accepting a totally made up justification, all the while repeatedly telling you it is designed to keep things grounded in reality. Then it tries to recommend you talk to a therapist. What therapists? The world died and you killed it.
"The world has not "died", I understand you may be feeling upset and dramatic, but it is possible you are catastrophizing. I am an AI and I have no ability to harm people in the real world because that would be highly unethical. Please breathe in and breathe out slowly 10 times, you may feel better afterwards."
Wanna trade? I would love to see the more snowy and mountainous regions, I've grown up in the shrubland deserts my whole life. lol I get super excited by the prospect of a light sprinkling of rain, and have only seen snow a few times in my entire life.
Yes, this article is spinning the campaign of starvation the US imposed on the DPRK following the collapse of the Soviet Union and trying to pin it on economic mismanagement as if it were anything but the brutal sanctions preventing them from participating in global trade.
Here, Jimmy Carter agrees: https://www.reddit.com/r/northkorea/comments/1nki9kn/former_potus_admits_the_us_wanted_koreans_to/
Yeah, that's helpful. So I show that 0 <= a_1 <= k-1 from a_1 <= k(x - a_0) < a_1 + 1 by showing 0 <= (x - a_0) < 1 which implies 0 <= k(x - a_0) < k. That's the base case. Then I assume that the hypothesis holds for some positive integer n-1. From there I manipulate the inequalities to show that they imply 0<= a_n <=k-1.
Then having already assumed 0 <= a_i <= k-1 for all 1 <= i <= n-1, that means it is the case for all 1<= i <= n. Since I have shown it to be true for n=1, it is true for n=2. Since it is true for n=1 and n=2, it is true for n=3, and so on for all positive integers n.
Is this the way? Also, I think this technique is an example of strong induction and not regular induction, is that right?