What is a well founded Poset?

What is a well founded Poset?

In mathematics, a binary relation R is called well-founded (or wellfounded) on a class X if every non-empty subset S ⊆ X has a minimal element with respect to R, that is, an element m not related by sRm (for instance, “s is not smaller than m”) for any s ∈ S. In other words, a relation is well founded if.

Is every well ordered set well founded?

The well-ordering theorem, which is equivalent to the axiom of choice, states that every set can be well ordered. If a set is well ordered (or even if it merely admits a well-founded relation), the proof technique of transfinite induction can be used to prove that a given statement is true for all elements of the set.

Was well-founded?

If you say that a report, opinion, or feeling is well-founded, you mean that it is based on facts and can therefore be justified.

Is well-founded hyphenated?

Tips: When something is well-founded, it is based on facts or solid evidence. Used after a verb, it is not hyphenated.

Is a total order a well Order?

A totally ordered set in which every non-empty subset has a minimum element is called well-ordered. A finite set with a total order is well-ordered. All total orderings of a finite set are, in a sense, the same.

Is well-founded meaning?

having a foundation in fact; based on good reasons, information, etc.: well-founded suspicions.

Was founded or was found?

It was found” or ” It was founded”? Both are correct, but they mean different things. “Found” is the past tense of “to find.” As in, if you are searching for something you will be happy when you find it. “Founded” is the past tense of “to found,” which means to establish something, like a company.

Is it well-founded or well-founded?

Tips: When something is well-founded, it is based on facts or solid evidence. Used after a verb, it is not hyphenated. See usage examples.

Is it well established or well established?

Well established or well-established? The approach is well established. It is a well-established approach. Use the hyphen when the expression occurs before the noun it modifies.

Are natural numbers totally ordered?

The natural numbers form an initial non-empty totally ordered set with no upper bound. The integers form an initial non-empty totally ordered set with neither an upper nor a lower bound.

Which sets are well-ordered?

In general, a set (such as N) with some order (<) is called well-ordered if any nonempty subset has a least element. The set of even numbers and the set {1,5,17,12} with our usual order on numbers are two more examples of well-ordered sets and you can check this.

Does well-founded have a hyphen?