Sentence examples for formal number from inspiring English sources

We do not know how Xenocrates understood addition: perhaps as a sort of map telling you that if you are on the unique formal number 2 and you want to add the unique formal number 3 to it, you cannot, strictly speaking, do that, but taking three steps on in the series will get you to the unique formal number 5, and that is what '2 + 3 = 5' really means.

After being assigned a case-filing number,20 a case then obtains a formal number, which is similar to an identity number.

And furthermore there is only one formal number for each of the numbers 2, 3, 4, etc., where there are indefinitely many instances of each among the mathematical numbers.

The architecture and the mode of operation of SHUNYATA are illustrated in detail by SHUNYATA's proof of Gödel's incompleteness theorem which says that every formal number theory contains an undecidable formula, i.e., neither the formula nor its negation are provable in the theory.

In trying to understand what Aristotle tells us about formal numbers, it is necessary to bear in mind the fundamental distinction he draws between formal numbers and mathematical numbers: both are, according to Aristotle, composed of units, but formal numbers are composed of very strange units, such that those in one formal number cannot be combined with those in any other.

The ω rule is an analogue in the λ-calculus of the rule of inference under the same name in formal number theory, according to which one can conclude the universal formula ∀xφ provided one has proofs for φ(x := 0), φ(x := 1), ….

That's a potential market of many hundreds of millions of users, and although the company hasn't released any formal numbers, it's safe to say that it's already really big, and likely to become even more so.

In other words, since he thinks that mathematics can be done with formal numbers, he feels it acceptable to call formal numbers mathematical numbers.

The position that there are both formal numbers and mathematical numbers Aristotle ascribes to Plato.

There are what he refers to as formal numbers, one for each numeral; these are the (Platonic) Forms for numbers.

Speusippus rejects the formal numbers (and the entire theory of forms along with them; see the entry on Speusippus).