Understanding Sets: Simplifying a Confusing Explanation and Question

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Typeset text: For any A ⊆ Z, there is a y ∈ Z such that for all x ∈ A, x ≥ y. Solution: False. Such a y only exists when A has a lower bound. It won't work if A continues towards negative infinity, e.g. if A contains all the odd integers.


I'm not quite understanding the explanation, or what the question is even asking. Anyone care to politely put it in simpler terms? Or in words or in a way that would make it easy for me to see?
 
hi mohabitar! :wink:

it's saying that it's not true that any subset of the integers has a lower bound …

for example, the negative odd integers have no lower bound :smile:
 
Hmm ok so that works for the solution, but what if that wasnt there. How would I be able to tell what the question is asking? How would you have been able to see it had the solution not been there?
 
hi mohabitar! :smile:

(just got up :zzz: …)
mohabitar said:
Hmm ok so that works for the solution, but what if that wasnt there. How would I be able to tell what the question is asking? How would you have been able to see it had the solution not been there?

In English, the question says "For any subset A of Z, there is no element y of Z such that y is less than (or equal to) every element of A."

Why do you not understand the question that way? :confused: