Combining Philosophers
Ideas for Jacques Lenfant, William D. Hart and Jeffrey H. Sicha
expand these ideas
|
start again
|
choose
another area for these philosophers
display all the ideas for this combination of philosophers
9 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers
|
17423
|
The essence of natural numbers must reflect all the functions they perform [Sicha]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
|
13463
|
There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD]
|
|
13492
|
Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD]
|
|
13459
|
The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD]
|
|
13491
|
The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD]
|
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
|
13446
|
19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD]
|
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
|
17425
|
To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha]
|
|
17424
|
Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
|
13509
|
We can establish truths about infinite numbers by means of induction [Hart,WD]
|