# Denoting the Largest Member of a Set: Symbols & Techniques

• bomba923
In summary, to denote the largest member of a set, one can use the notation max(A). This is the accepted way of expressing the concept of the largest member of a set. It is important to note that the maximum and the supremum may differ, as the supremum can exist even if the maximum does not, especially in the case of infinite sets. However, in the case of finite sets, the maximum will always exist.
bomba923
Let's say I have a set {A}. How do I denote the largest member of that set?
For example, let's say I have a solution set of discrete values. How do I denote the largest solution?

Basically, with any set, how do I denote the largest member of that set? What symbol/s do I use !?

What's wrong with something like $$max(A)$$??

That is the formal/accepted way of expressing it (the largest member of a set), right?

Do maximums differ from least upper bounds (supremums)? The definitions I found didn't clear this up. Edit: Eh, because I was going to say supremum.

AFAIK, the maximum of a set must necessarily be a member of the set as well. So for example, {1 - 1/n; n a natural} has a supremum, but no maximum.

Muzza is absolutely correct.

given a set (presumably of real numbers) there is no reason for that set to even have a greatest element, even if it is bounded above (ie all elements are less than some constant K). The sup is the smallest such K that bounds them above, and this is the max if and only if K is an element of the set.

Note, that this only applies to infinite sets. Any finite set of points must have a maxmimum.

## 1. What is the symbol used to denote the largest member of a set?

The symbol used to denote the largest member of a set is the capital letter "U" with a horizontal line on top, known as the "union" symbol.

## 2. How do you find the largest member of a set using the "union" symbol?

To find the largest member of a set using the "union" symbol, you simply take the union of all the elements in the set and the result will be the largest element in the set.

## 3. Are there any other symbols or techniques used to denote the largest member of a set?

Yes, there are other symbols and techniques that can be used to denote the largest member of a set. One technique is to simply write the word "max" before the set, which stands for the maximum value. Another symbol that can be used is the capital letter "S" with a horizontal line on top, known as the "supremum" symbol.

## 4. Is it necessary to use symbols or techniques to denote the largest member of a set?

No, it is not necessary to use symbols or techniques to denote the largest member of a set. These symbols and techniques are simply a way to represent the concept of finding the largest element in a set in a more concise and mathematical way.

## 5. Can the concept of finding the largest member of a set be applied to all types of sets?

Yes, the concept of finding the largest member of a set can be applied to all types of sets, as long as they have a defined order or ranking system. This includes sets of numbers, letters, or any other types of elements.

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