Let Omega ={An: N=1,2,3,...}, where An={0, n, n+1, n+2...}
A) Find Intersection Omega and prove your conjecture. B) Find Union Omega and prove your conjecture.
I'm completely lost on these types of questions. I have reached out to our group chat for class and the teacher for help with no responses yet
The sad thing is I think you don't understand the class material as presented. There isn't much to these problems other than comprehension.
In this $A_1 = \{0,1,2,3,4,5,,.....\}$ and $A_2 = \{0, 2,3,4,5,6,7,.......\}$ and $A_3=\{0,3,4,5,6,.....\}$ and so on.... $A_{137} = \{0, 137, 138, 139,....\}$ and $A_{56789}= \{0, 567889, 567890, 567891,....\}$ and $A_k = \{0, k, k+1, k+2, k+3,.....\}$.
$\Omega$ is a collection of all these sets. The question is asking what is the intersection of all these sets.
The intersection refers to the set you get when you consider all the elements that are contained in each and every set. So what elements do the sets $ \{0,1,2,3,4,5,,.....\}$ and $ \{0, 2,3,4,5,6,7,.......\}$ and $\{0,3,4,5,6,.....\}$ etc. all have in common? What is the set that contains all the elements in common?
Hint: $1$ is not in the intersection as it is not in all the sets; $1$ is not an element of $A_2, A_3$ and so on. And $2$ is not in the intersection as $2$ is not in $A_3 = \{0,3,4,5,6,....\}$.
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So this is what the question is asking you to do.
