12489 | If there were real infinities, you could add two together, which is ridiculous [Locke] |
19406 | I strongly believe in the actual infinite, which indicates the perfections of its author [Leibniz] |
13190 | I don't admit infinite numbers, and consider infinitesimals to be useful fictions [Leibniz] |
10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
13464 | Cantor proposes that there won't be a potential infinity if there is no actual infinity [Hart,WD on Cantor] |
15923 | Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Lavine on Poincaré] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
11025 | Infinite cuts and successors seems to suggest an actual infinity there waiting for us [Read] |
10125 | The classical mathematician believes the real numbers form an actual set [George/Velleman] |