请教数学分析习题

elimqiu · 发表于 2010-9-24 21:44

The way of getting through those topics is to write things explicitly according to definitions and then manipulate them according to established laws.
Those topics are quite mechanical, although a little abstract, but not really tough.

kindlychung · 发表于 2010-9-25 01:49

Love explanation. Many thanks.
Here comes another.
Since N is an inductive set and N is infinite, why can';t induction be used to prove this?

elimqiu · 发表于 2010-9-25 07:50

Math Induction can only be used to show proposition with parameter n is true for all n in N. Since ∞ is not in N, (b) cannot be proven by induction
(c) the equality in (b) is valid:

kindlychung · 发表于 2010-9-26 01:08

Why is infinity not in N? n can get infinitely large.

elimqiu · 发表于 2010-9-26 01:57

下面引用由kindlychung在 2010/09/26 01:08am 发表的内容：
Why is infinity not in N? n can get infinitely large.

But not infinite itself

kindlychung · 发表于 2010-9-26 13:20

What do you mean "infinite itself"? Please give a definition.

elimqiu · 发表于 2010-9-27 13:05

N does not contain infinite itself

kindlychung · 发表于 2010-9-27 13:55

Again, we need to agree on the definition of "infinite itself", to determine whether it';s contained in a set, we have to first define what it is.
After that I';d like to know what set contain infinite itself? Does R?

elimqiu · 发表于 2010-9-27 14:06

Good thoughts. But since infinite is not a number in your book, therefore N does not contain it and so induction does not work here.

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请教数学分析习题