Ideas of R Kaplan / E Kaplan, by Theme

[American, fl. 2003, Husband and wife who have both taught mathematics at Harvard University.]

idea number gives full details    |    back to list of philosophers    |     expand these ideas
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Using Choice, you can cut up a small ball and make an enormous one from the pieces
6. Mathematics / A. Nature of Mathematics / 3. Numbers / b. Types of number
1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals
6. Mathematics / A. Nature of Mathematics / 3. Numbers / g. Real numbers
The rationals are everywhere - the irrationals are everywhere else
6. Mathematics / A. Nature of Mathematics / 3. Numbers / q. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million