Ideas of R Kaplan / E Kaplan, by Theme
[American, fl. 2003, Husband and wife who have both taught mathematics at Harvard University.]
green numbers give 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
|
15717
|
Using Choice, you can cut up a small ball and make an enormous one from the pieces
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
|
15712
|
1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
|
15711
|
The rationals are everywhere - the irrationals are everywhere else
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
|
15714
|
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference
|
|
15715
|
'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
|
15713
|
The first million numbers confirm that no number is greater than a million
|