Then the x is the smallest element.

Let's do the general formulation.

Where it is actually nonsense, but usually you can also find it in such forms.

So let's assume we would have a part of this amount of the ordered quantity.

However, this part of the quantity is again a quantity of the ordered quantity,

and I would have been able to leave it out, but usually you find it in the form.

That's why it's so important.

So we take the element of a, which is the smallest element of a.

And the writing method, to make it a little more confusing, is

x is the minimum of a.

And that is actually a word that is used there.

So x is the minimum of a.

And then, if it only increases in size, if it increases for all y from a,

x is the smallest element or a minimum.

But it is one of potential 4.

So how many smallest elements can a quantity have?

All. They can all be equal.

That's a word, and not a formula.

That means if I have two smallest elements, then...

That fits, doesn't it?

They have to be equal.

And if I have two minimums of a, then one small one is equal to y, where x is a minimum.

On the other hand, y is equal to x, where y is a minimum.

So x is equal to y per antisymmetry.

That's true.

So there is only one smallest element.

And then there is the term of the minimum element.

Or, in other words, minimum in a.

Positive means that for all y from a, it is not equal.

We are talking about no equal.

Of course, it is not true that there is no element that is equal to x.

x itself is equal to itself.

And the statement is good, there is no other.

So if x is equal to x, then I don't want to do anything about it.

That's a minimal element.

Minimal elements are generally not clear.

For example,

the following quantity.

It is calculated that I have formulated the total quantity.

I now take a known partial order, namely x equals power set,

because it is a potential quantity, but I will show a certain expression.

Namely, the corresponding partial quantities of x, which are not clear.

So, the total quantity of the potential quantity is calculated, as always, by the equation.

What are the minimal elements of this quantity?

All one element.

And they are incomparable.

Minimal elements are not clear, but there is never a minimal element that is smaller than another.

The minimal elements always form what is called an anti-chain.

An anti-chain is a calculation of elements that are not comparable to each other in any direction.

Minimal elements will not play the role here.