[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 116
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Все понятно с Вами, alexeros. Я как-то сразу об этом и не подумал :)
Только вот насчет 0.9999(9) можно было и не писать. Это ж все равно единица. Нас бесконечные периодические дроби не пугают.
There's a limit, by the way, to both right and left.......
A little loosely: 92222/2 = 46111.
А 98888/8 = 12361. Lucky for you, you still have one at the end.
The funny thing is that your reasoning should be correct for three identical digits, but it probably isn't. Looking for a counterargument.
You're absolutely right, was a bit inattentive. Got the unit count wrong. :-)
However, the proof is rigorous. It's just that for twos there will be at least 3 units, not 4. For fours it's not 3, but 2. And for eights it's 1, not 2.
The writers of the problem are clever people. They didn't leave 4 identical digits at the end for nothing. Just enough to prove it. :-)
Well yes, AlexEro, just different sequences would be. I wrote the limit on the right to make it easier to see the point.
Why not 6666 or 8888? These cases have to be considered too, imho. And they are the ones that are confusing.
Can't you read to the end of the proof?
Well yes, AlexEro, just different sequences would be. I wrote the limit on the right to make it easier to see the point.
I wonder what you and AlexEro call the limit. Let me read the definition.
Dyck is the same as you, Yuri. Both by Cauchy and by Heine.
The whole quarrel has flared up over whether or not to explicitly specify that x -> x_0 means not just an arbitrary aspiration to x_0, but such that all x falls necessarily into the domain of the function D. Most have come to the conclusion that it is not necessary, but only sufficient that x_0 is the limit point of D.
So I gave an example where x_0 is a limiting point of D, and this D is countable, i.e. it consists of separate points.
MetaDriver, (1) могу удалить данные "о себе", я вижу уже некоторых это раздражает, в том числе и вас. (2) Мне вообще то пофигу, хотел найти людей по интересам.
(3) Судя по всему вы изучали психологию. Интересно, кого именно? Напишите, если хотите, я в этой области знаю несколько больше, чем некоторые другие.
1) Don't you dare! :) Maybe some people are annoyed, I don't know. On the contrary, I'm pleased.
2) That's great.
3) OK, I'll write. Tomorrow. It's past my bedtime now.
ps. I'm sorry if you were offended. Maybe I went a little overboard with the "diagnostic humor". I was just hoping you didn't care and just wanted to have some fun. I'm sorry.
Yes, sort of. Also x=0, which is not in D, but is the limit point of D.
Ну да, AlexEro, просто разные последовательности будут. Я написал предел справа, чтобы легче была видна суть вопроса.
Yeah, I get it, I get it, just in case - just to clarify for the rest of us.