No.50 Referenced from ~ Part2 - Chapter 2 - Hard study 5-3-3 A proposition whose negation cannot be proven will surely be proven in time
But that was not the only question. The very content of the statement, "A proposition whose negation cannot be proved will surely be proved in time," is a claim that is difficult to comprehend. What kind of world is being considered? The example question of whether the decimal sequence of π contains 100 consecutive zeros may give us a glimpse of such a world. To roll a 6-sided dice and get a 1 twice in a row, you have to roll the dice 6^2+1 = 37 times. Similarly, if you roll a 10-sided dice 10^100 times, it is almost possible to get a 0 100 times in a row. (There is no regular decahedral, but there are decahedral dice with kite faces of the same shape. Or you can use a regular icosahedron instead.) As of 2019, the decimal sequence of π has been calculated to 31 trillion digits, which is equivalent to rolling a 10-sided die 3.1×10^13 times. Therefore, at the present time, the number of times the dice are thrown is still insufficient, but eventually, if you roll 10^100 times, then 10^200 times, you will almost always have the opportunity for 100 consecutive occurrences of 0. |