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The first one , since
OH!!!!!!! You can replace
NEVER THOUGHT OF THAT!!!!Oh , I see .. lol~
I checked my book , it said the answer is
If A={1,2,3} the bi-function is 2x+1 , then B={3,5,7}
If P(x)=(x-1)(x-2)(x-3)
Then P(A)={0} , P(B)={0,24,120}
I think this statement is a little weird.
I have trouble with second derivative , I am not sure if I have skipped some
important rules , please help me step by step or point out my error.
here is what I did with (1)
Yah , right , your method shows that whatever S_n be , there is a y to avoid it.
What I wanted to do was , to show that there is always one new real number between two real number , if the set of real is countable, then between two element , there is always a new element in Real , but not in the set , contradict with the definition of the set which contains all real numbers. thus real number is uncountable.
The proof of Rational being countable is given in the book
this question is from the Rudin's book , he just simply mention there is a one-to-one correspondence between S and N if S is countable, and that is .It's more like a handbook than a textbook.
and I haven't learned about Cantor's diagonal argument ,About proving the open interval (0, 1) is uncountable , Can I do it this way?
Assume it's countable then the set
Prove whether the set of all irrational real numbers countable.
I think it's uncountable
Then I think the set of rational number is countable and closed
then its complement the set of irrational is open , thus uncountable.
I don't know If I have misunderstood these math concepts.
Please give a proof
I am looking for some thing about Differential Geometry now . I always learn some from here and some from there , never go deep into one.
all you need to do , is to put the divisor up side down and multiply
I am interested in finding the explanation for space time , black hole sth like that.
Yah , I am going to try that one , thank you . and , I always wanted to learn Theoretical Physics someday , do u know what kind of math , I have to be equiped with?
My book is Principles Of Mathematical Analysis by Walter Rudin , and I find his proofs very confusing . Thanks again!
Did you guys feel confused at the first time? the whole thing is so abstract , my textbook doesnt have a graph and I have to learn it by myself .
Thanks a lots . But like this kind of expression metric space (M, d), What does it mean , I've never seen it before.
I am really confused about basic topology, What does it mean by E is closed if every limit point of E is a point of E.
and How to use the notation of neighborhood to prove things .
Suppose
where X is a metric space , how can E be relative to Y and not to X at the same time.you mean which field in math? Geometry? Algebra? or ....?
Here is what I think about the second
First ,
rearrange it , get
Obviously
Then
And
Then ...Still working on it.
I dont think you did wrong , cuz 4(3,0,4)=(12,0,16)
Too many unknown , I use trick to eliminate them , I dont know if it's correct tho.