一些逻辑训练的谜题：娜塔莎、十二点钟和茶
我的同事，娜塔莎喜欢小孩子，就给他们出了一些题。而我在十二点钟和娜塔莎闲谈时，总会为她补充一些，而她也觉得这还不错。到了下午，我们一起喝茶时，我们会把饼干放在鸟笼边，猫头鹰则会将其啄成碎片。我们的生活就是这样悠闲地度过的，和这所大学里的本科生的终日忙碌仿佛处在两个世界，他们没有心情欣赏校园里的建筑多么有艺术感，也看不见柳树和池塘蕴含着十四行诗——就算你不是莎士比亚也可以发现——只等着被抓出来和记录下来，但我们是刚好反过来的。
在这里，我会归纳一些我们设计的，助益于逻辑能力的谜题。
在这里，我会归纳一些我们设计的，助益于逻辑能力的谜题。
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>>If I may probe further, could you please help me u...
The infinities are different, you see, it's possible to assign every natural number with a real number, obviously. But we can't assign every real number with a natural number without repeating, otherwise we'll be able to give every real number bigger than 0 smaller than 1 a natural number to make the order.
Let's assume we can give all real numbers in (0,1) a name associated with a unique natural number, then we can write them like,
the 1st number 0.a(1,1)a(1,2)a(1,3)a(1,4)a(1,5)a(1,6).......
the 2nd number 0.a(2,1)a(2,2)a(2,3)a(2,4)a(2,5)a(2,6)......
.......
the a(x,y) above means a digit(ranged from 0 to 9) of such number, a(1,1) means the first digit after the decimal separator of the first number for example. All numbers in this list are supposed to cover all the real numbers in (0,1).
Then let's check out this number
W=0.b1b2b3b4b5....
where b1=a(1,1)+1(if a(1,1) is 9, then let b1 be 0, the same works below)
b2=a(2,2)+1
b3=a(3,3)+1
.....
W is well defined but different from any given kth number at the digit bk, so W won't be in the list, contradicting to our assumption.
just like the case above, we say the cardinality of the R set is bigger than the N set, because we can give each element in the latter one specific and unique element in the former, but we can't do the contrary. And obviously, when two lines are not resembling, we need two or more steps to draw them all. And you see, we need to draw a total number of both dots and lines(of different directions or locations) even bigger than the infinity of natural numbers, while our steps are always like, step 1, step 2, step 3 and so on, thus its cardinality is the same as natural numbers.