[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 117

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Mathemat писал(а) >>

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.

 
Mathemat >>:

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 :)

alsu >>:

Well, yes, if for example c=1, then a and b can be any:)))

Mathemat >>:

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.:)

 
The murovane is shaped like a cube, the ribs of the cube are constantly preceded by fighting murovines, so that the number of murovines coming to an edge equals the number of murovines going out, number the ribs from 1 to 12, 2 different ribs should not have the same number.
 
the end of the 12th must be the beginning of the 1st?
 
sanyooooook >>:
Муровейник имеет форму куба,


and ants are shaped like spherical horses )
 
Mischek >>:


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 ))))))

 
sanyooooook >>:

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 (

 
Mischek >>:


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.

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