What is this supposed to mean?mtayab1994 said:Homework Statement
{1/x+1/y / (x,y) in (IN*)^2} subset of ]0,2]
mtayab1994 said:Homework Equations
The Attempt at a Solution
When x=y=1 u get a sum of 2 which is in ]0,2] and for any x and y greater than 1 u get a sum between 0<sum≤2.
It's a simple problem but i just don't know how to show the proof. Some help please.
micromass said:Do you mean to say that
[tex]\{1/x+1/y~\vert~x,y\in \mathbb{N}\setminus\{0\}\}[/tex]
That would make sense...
So you need to show that
[tex]\frac{1}{x}+\frac{1}{y}\leq 2[/tex]
for all naturals x and y. Maybe use the fact that
[tex]\frac{1}{x+1}\leq \frac{1}{x}[/tex]
and do induction??
A subset in set theory is a set that contains elements from another set. It is denoted by the symbol ⊆ and read as "is a subset of". For example, if set A = {1, 2, 3} and set B = {1, 2}, then B is a subset of A.
A subset is determined by checking if all the elements in the subset are also present in the original set. If the subset contains any elements that are not in the original set, then it is not a subset. For example, if set C = {4, 5}, then C is not a subset of set A from the previous question because A does not contain the elements 4 and 5.
The purpose of proving a subset in set theory is to formally establish that a smaller set is contained within a larger set. This is important in mathematical proofs and logical arguments, as it helps to build a solid foundation for further reasoning and conclusions.
The notation for the set of all real numbers between 0 and 2 is ]0,2[. The square brackets indicate that the endpoints, 0 and 2, are not included in the set. This is known as an open interval notation.
To prove that a set is a subset of ]0,2], we need to show that all the elements in the set are between 0 and 2, including the endpoints. In other words, all the elements in the set must be greater than or equal to 0 and less than or equal to 2. This can be done by listing out all the elements in the set and checking if they satisfy this condition.