Where does element collide?

A substance made of atoms that all share the same number of protons, the property that fixes its place on the periodic table. In the IUPAC Compendium of Chemical Terminology an element is defined by atomic number: hydrogen is every atom with one proton, oxygen every atom with eight, whatever the isotope. The referent is a kind of matter in the physical world, and membership is settled by counting protons, not by choice or argument. Scerri's history of the periodic table shows the ordering is a discovered regularity, not a convention: the elements fall into place by proton number whether or not anyone tabulates them. This meaning shares only the word with the others; a proton count says nothing about a set, a legal claim, or the four classical roots.[1][2]

Unit

A kind of matter fixed by proton number

Recovery means

Not applicable

Measured by

Atomic number, read from the count of protons in the nucleus

An object that belongs to a set, related to it by the membership relation written with the symbol for is an element of. In Halmos's Naive Set Theory everything hinges on this single primitive: to say x is an element of A is to say x is one of the things A collects, and a set is determined entirely by which objects are its elements. The referent is abstract and the relation is stipulated, not measured: an object is an element of a set because the set was defined to include it, and the same object can be an element of one set and not another. Unlike a chemical element, nothing about the object itself makes it an element; only its relation to a chosen collection does.[3]

Unit

An object standing in the membership relation to a set

Recovery means

Not applicable

Measured by

Whether the membership relation holds between an object and a set, by the set's definition

One of the components a party must prove for a cause of action or a crime to be made out, each of which has to be established or the claim fails. The Restatement (Second) of Torts sets the elements of negligence at section 281: a duty owed, a breach of that duty, a causal link, and resulting harm. Keeton and colleagues treat these as separate requirements carried by the plaintiff's burden of proof, so that missing any one defeats the whole. The referent is a requirement inside a legal test, and what makes something an element is doctrine plus the burden of proof, not a proton count and not a chosen set. The meanings touch only at the idea of a necessary part; the parts here are things a court must find, not objects or atoms.[4][5]

Unit

A component of a legal test that must be proven

Recovery means

Not applicable

Measured by

Whether each required component is established to the applicable standard of proof