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UncertaintyAjay
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Could anyone recommend some books or exercises to practice proofs? Or even post some theorems to prove?
Thanks in advance,
Ajay
Thanks in advance,
Ajay
What field of mathematics and what level are you interested in?UncertaintyAjay said:Or even post some theorems to prove?
UncertaintyAjay said:I'll be headed to university this fall. I am familiar with calculus, really basic number theory, geometry, algebra etc.
Ok. The following is perhaps more about notation and careful reading than about mathematics proper, but here it is:UncertaintyAjay said:I'll be headed to university this fall. I am familiar with calculus, really basic number theory, geometry, algebra etc.
Does that mean that you know what a countable set is?UncertaintyAjay said:I am also familiar with a few proof strategies like induction
I assume this is for x and r both belonging to real numbers?Assume the above statement to be true. Then for any element of the set S {r:r>0} there must be another element smaller than it. I.e there is no smallest element of S.( Now i am a bit stuck, I know that there is no smallest element in the set of real numbers, so the statement is true,but I haven't the foggiest idea how to prove it. I'll think over and see if there is another approach to the proof as well)Krylov said:{x>0:x<r∀r>0}≠∅{x>0:x<r∀r>0}≠∅\{x > 0 \,:\, x < r\,\forall\,r > 0\} \neq \emptyset.
I do. The set of natural numbers,prime numbers, odd numbers, even numbers etc. are countably infinite. Real numbers, irrational numbers etc. are not.Krylov said:Does that mean that you know what a countable set is?
UncertaintyAjay said:I do. The set of natural numbers,prime numbers, odd numbers, even numbers etc. are countably infinite. Real numbers, irrational numbers etc. are not.
Yes, that was implicit in the ##>## sign, but you are very correct.UncertaintyAjay said:I assume this is for x and r both belonging to real numbers?
OkUncertaintyAjay said:I'll think over
Beautiful, then I already have some other calculus-flavored exercises in mind.UncertaintyAjay said:I do. The set of natural numbers,prime numbers, odd numbers, even numbers etc. are countably infinite. Real numbers, irrational numbers etc. are not.
I was thinking about this one, but it may be a bit too difficult, since a number of steps are required. However, in principle it should be doable.UncertaintyAjay said:Bring it on. I haven't been this excited in ages.
UncertaintyAjay said:I'll be headed to university this fall. I am familiar with calculus, really basic number theory, geometry, algebra etc.
The purpose of "Proof Practice Ideas" is to provide a comprehensive guide for practicing and improving one's skills in mathematical proof writing. It includes a selection of books, exercises, and theorems that are commonly used in the field of mathematics.
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