Combining Texts
Ideas for
'The Evolution of Logic', 'Must We Believe in Set Theory?' and 'The Inference to the Best Explanation'
expand these ideas
|
start again
|
choose
another area for these texts
display all the ideas for this combination of texts
8 ideas
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
|
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]
|
|
13463
|
There are at least as many infinite cardinals as transfinite ordinals (because they will map) [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 / 5. The Infinite / a. The Infinite
|
10491
|
Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
|
|
13509
|
We can establish truths about infinite numbers by means of induction [Hart,WD]
|
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
|
10483
|
Mathematics and science do not require very high orders of infinity [Boolos]
|