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Full Idea
The usual formal laws of arithmetic are the Commutative Law [a+b=b+a and axb=bxa], the Associative Law [(a+b)+c=a+(b+c) and (axb)xc=ax(bxc)], and the Distributive Law [a(b+c)=ab+ac)].
Gist of Idea
The formal laws of arithmetic are the Commutative, the Associative and the Distributive
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], IX)
Book Ref
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.94
| 13155 | If you add one to one, which one becomes two, or do they both become two? [Plato] |
| 9865 | Daily arithmetic counts unequal things, but pure arithmetic equalises them [Plato] |
| 16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant] |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| 14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| 21665 | The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber] |