Content deleted Content added
JumpDiscont (talk | contribs) →Contradiction.: Reply |
→Contradiction.: Reply |
||
Line 1,409:
:::::::More generally, for all lists of numbers, if [for all sufficiently large n, the n-th number in the list has a non-zero n-th digit after the decimal place] then for all sufficiently large n, at most n numbers in the list have only n digits after the decimal point, even though there are 10^n numbers (not necessarily all in the list, and indeed for such n they can't all be in the list) with only n digits after the decimal point.
:::::::[[User:JumpDiscont|JumpDiscont]] ([[User talk:JumpDiscont|talk]]) 04:18, 30 April 2025 (UTC)
::::::::A thought experiment and an analogy to a matrix. A drum counter like the ones used to have on car odometers, i.e. each column of the matrix is a drum with digits from zero to nine. That is, after the decimal point there is an infinite number of drums, the digits on the drums arranged in a line create a number with an infinite decimal expansion. The first drum after the decimal point rotates changing the digit, e.g. every second, the second drum rotates ten times faster than the first drum, the third drum rotates ten times faster than the second drum, the fourth drum rotates ten times faster than the third drum, etc. each subsequent drum rotates ten times faster than the previous one. After a full rotation of the first drum, i.e. after ten seconds, the counter will create all possible combinations of digits in the line, which will ultimately create all possible numbers from zero to one written in the decimal positional system. [[User:Krzysztof1137|Krzysztof1137]] ([[User talk:Krzysztof1137|talk]]) 21:53, 29 June 2025 (UTC)
| |||