Andrax said:we have E=(a+b)/ab (a,b)EN*
1/ prove that E C ]0,2] (i already duid that )
2/ is ]0,2] E E? shelp me in this one!
Homework Equations
The Attempt at a Solution
x [itex]\in[/itex] ]0,2] [itex]\Rightarrow[/itex] x [itex]\in[/itex] E
E means ##\in## and N* means the positive integers, I believe.LCKurtz said:If E=(a+b)/ab what does EN* mean?
I second that.LCKurtz said:What does ]0,2]E E mean? Please state your problem with proper notation.
Andrax said:well sorry didn't find the proper notations in the advanced mode umm any solution?
Andrax said:well sorry didn't find the proper notations in the advanced mode umm any solution?
Ray Vickson said:You could try using words:
E = {(a+b)/(ab): a,b positive integers}. And "is ]0,2] a subset of E?"
or
E = {(a+b)/(ab): a,b,in N*}, and "is ]0,2] subset E?"
RGV
In other words, you want to show that if [itex]0< x\le 2[/itex], the x= (a+ b)/(ab) for some positive integers a and b. [itex]\sqrt{2}[/itex] lies between 0 and 2 doesn't it?Andrax said:I want to prove that ]0,2 is a subset of E E = {(a+b)/(ab): a,b,in N*}, and "is ]0,2] subset E?"
HallsofIvy said:In other words, you want to show that if [itex]0< x\le 2[/itex], the x= (a+ b)/(ab) for some positive integers a and b. [itex]\sqrt{2}[/itex] lies between 0 and 2 doesn't it?
Set theory is a branch of mathematics that deals with the study of sets, which are collections of objects or elements. It provides a foundation for all of mathematics and is used to define and analyze concepts such as numbers, relations, functions, and infinity.
A set is a well-defined collection of objects or elements. These objects can be anything, such as numbers, letters, or even other sets. Sets are typically denoted by curly braces { } and each element is separated by a comma. For example, the set of even numbers can be written as {2, 4, 6, 8, ...}.
The three basic operations in set theory are union, intersection, and complement. Union combines all the elements from two or more sets, intersection finds the common elements between two or more sets, and complement finds all the elements that are not in a given set.
A set is a collection of elements, while a subset is a set that contains some or all of the elements of another set. In other words, all the elements of a subset are also elements of the larger set, but not all elements of the larger set are necessarily in the subset.
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