My question is this: If two sets are equal does that mean that they are necessarily equal?
To supplement bobpursley's previous comment,
HUH ?
I suppose you mean to say:
"My question is this: If two sets are equal does that mean that they are necessarily equivalent?"
The answer is yes. Can you explain to us why this is so?
(Study Bob's previous statements to help you answer why)
To determine if two sets are equal, we need to compare their elements. If two sets have exactly the same elements, with no repetition and no additional or missing elements, we can say that they are equal.
If you want to check if two sets are equal, you can follow these steps:
1. Compare the number of elements in the sets. If they have a different number of elements, they cannot be equal.
2. Compare each element of one set to every element of the other set. If there is any element that does not have a match in the other set, or if the sets have different elements, they are not equal.
3. Repeat the comparison for both sets. Even if one set is a subset of the other, they will only be equal if both sets are subsets of each other.
To clarify, the term "necessarily" means something that is always true or must happen. So, if two sets are equal, they are necessarily equal.