[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 117
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Yes, sort of. Also x=0, which is not in D, but is the limit point of D.
Well, if so, then of course there is a limit.
But in this case, too, you get an absurdity. Your proposed variant with (-1) then has a domain as a countable set and the function on this set takes the same value at all points. Can we call it space, area of definition and convergence ?
If it is explicitly stated that, say, x belongs to D, then why not - even in such an exotic case. Opponents on that forum think that if it is not explicitly stated, then it is assumed that the default values of x must fall into D.
I apologise for the off-topic. I've been racking my brain for a long time.
There are 4 currencies, 6 currency pairs. For example gbp, eur, usd and jpy.
How many pairs can be held simultaneously in one direction at most? I haven't found a solution yet.
Следующая:
Доказать, что существует бесконечно много таких троек натуральных чисел a, b, c, что a! = b! · c!.
Надеюсь, что эта задачка будет посложнее последних.
P.S. Пардон, ошибся. Она простая :)
Well, yes, if for example c=1, then a and b can be any:)))
Let's assume that this is a trivial case.
Find the non-trivial ones (not necessarily all of them, just an infinite number is enough).
P.S. By the way, c=0 also fits
.It's not natural, though.
Solution:
We set c arbitrarily. Let b=c!-1, then b!*c!=(c!-1)!*c!=(c!)!
Now, taking a=c!, we obtain the required equality.
Since c is chosen arbitrarily, there are an infinite number of possible variants, h.t.c.:)
Муровейник имеет форму куба,
and ants are shaped like spherical horses )
а муравьи форму сферических коней )Come on, you can't imagine a cubic murovane, that's the easiest part of the problem, it was harder for me when I tried to formulate the problem, and even harder when I've been solving it for 3 years ))))))
да ладно ты что кубический муровейник представить не можешь чтоль, это самое простое в этой задаче, сложне было мне когда пытался сформулировать условие задачи, и еще сложнее когда решал эту задачу в течении 3 лет ))))))
Relax
There's a smiley face.
I get it - no solution (
Спокойно
Там смайлик стоит
У меня получается - нет решения (
There's a solution, I've been working on it for three years, but I've lost it somewhere.