For the sake of checking the above claim I went to Tao's blog and discovered the following comment (not quite what was asked for, but alas): "There’s something I just don’t understand, why bother with all this crap? There are much easier ways to earn 1 million than go for a millennium problem. What is the point of math at all? This world is all about shallowness, money, status, only a naive person who never grew out of that innocent teen mentality would waste his life on these useless and intractable problems. You publish some result that takes years in the making, only to have less than 50…
But, to be honest, I put more effort into teaching throughout my career because I wanted to make a difference, and having a handful of people who would read my best papers wasn't infinitely fulfilling.
And then out of nowhere, someone starts asking me questions in a comment, with questions almost nothing to do with the original question. Agh!
I think I'm having a bad day. Even ignoring the world.
You know, a while back, someone on Reddit tried to tell me that the reason Chaucer (14th cent) spoke differently than we do is because he didn't have access to a dictionary
The Supreme Court on Criminal Law, 1950 to 1966, with a Supplement Incorporating Cases from January to December 1967: The expression "fraud" involves two elements, deceipt, and either injury to the person deceived or advantage to the author of the deceipt as a result of the deceipt or both.
someone on reddit told me that every redditor is a liar
I think this edit was correct (at least in the context of the answer) and should not have been rejected: math.stackexchange.com/review/suggested-edits/1296593. Is it possible to re-evaluate the suggested edit? The calculated value doesn't hold with the current expression in the answer.
Tommy’s amazing new lim for the golden number ?!
While we were playing a game of chess I asked my friend tommy if he knew a nice limit for the golden number.
Immediately he answered this
$a_1 = 1.$
$a_2 = 2$
For integer $ n > 2 : $
$$a_n = \frac{a_{n-1}(a_{n-1} + \frac{1}{3})}{a_{n-2}}.$$
...
the axiomatization of mathematics was just an elaborate cover-up to hide that - deep down - we don't know anything and all that we pretend to be knowledge is inherently self-referential and based on implicit pretense
@AkivaWeinberger With 2^k: https://www.wolframalpha.com/input/?i=10%21%2F2%5E5+-+sum+%28-1%29%5E%28k%2B1%29%285+choose+k%29%2810-k%29%21%2F2%5E%7Bk%7D%2C+k%3D1+to+5 With 2^{5-k}: https://www.wolframalpha.com/input/?i=10%21%2F2%5E5+-+sum+%28-1%29%5E%28k%2B1%29%285+choose+k%29%2810-k%29%21%2F2%5E%7B5-k%7D%2C+k%3D1+to+5
Either the given statement is incorrect or the calculated answer is. Also, if you look at one of the comments of the answer, it looks like 2^{5-k} is correct.
Zero sharp was defined by Silver and Solovay as follows. Consider the language of set theory with extra constant symbols c1, c2, ... for each positive integer. Then 0# is defined to be the set of Gödel numbers of the true sentences about the constructible universe, with ci interpreted as the uncountable cardinal ℵi. (Here ℵi means ℵi in the full universe, not the constructible universe.)
In fact, I'd go a little further and say that cardinal properties are seldom absolute. Remember, "absolute" means that the property's truth value doesn't change when you move between larger and smaller models.
Even being a cardinal is not absolute. For example, it's fairly straightforward to con...
Also I feel like the # symbol should just be a hash. "#YOLO" is a tag with a hash in it, aka a hashtag. If # were a hashtag, "#YOLO" would be a hashtagtag!
Tommy’s amazing new lim for the golden number ?!
While we were playing a game of chess I asked my friend tommy if he knew a nice limit for the golden number.
Immediately he answered this
$a_1 = 1.$
$a_2 = 2$
For integer $ n > 2 : $
$$a_n = \frac{a_{n-1}(a_{n-1} + \frac{1}{3})}{a_{n-2}}.$$
...
