more from this thinker     |     more from this text

Single Idea 10863

[filed under theme 27. Natural Reality / C. Space / 3. Points in Space ]

Full Idea

Cantor proved that one-dimensional space has exactly the same number of points as does two dimensions, or our familiar three-dimensional space.

Gist of Idea

Cantor proved that three dimensions have the same number of points as one dimension

Source

report of George Cantor (works [1880]) by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.14

Book Ref

Clegg,Brian: 'Infinity' [Robinson 2003], p.183

The 13 ideas with the same theme [minimal units that make up space]:

10863 Cantor proved that three dimensions have the same number of points as one dimension [Cantor, by Clegg]
16962 Whitehead replaced points with extended regions [Whitehead, by Quine]
14160 Space is the extension of 'point', and aggregates of points seem necessary for geometry [Russell]
18970 The concept of a 'point' makes no sense without the idea of absolute position [Quine]
17811 The natural conception of points ducks the problem of naming or constructing each point [Kreisel]
17707 We should regard space as made up of many tiny pieces [Feynman, by Mares]
18257 Why should the limit of measurement be points, not intervals? [Dummett]
3334 Rationalists see points as fundamental, but empiricists prefer regions [Benardete,JA]
22922 We can identify unoccupied points in space, so they must exist [Le Poidevin]
22924 If spatial points exist, then they must be stationary, by definition [Le Poidevin]
8269 Points are limits of parts of space, so parts of space cannot be aggregates of them [Lowe]
4227 Surfaces, lines and points are not, strictly speaking, parts of space, but 'limits', which are abstract [Lowe]
17708 Maybe space has points, but processes always need regions with a size [Mares]