Talk:1234 (number)

Mock rational
Is the "first member of sequence to have a repeated digit in the first five after the decimal" property really interesting? The probability that a random decimal would have this property is more than 1/3, and it appears unrelated to the non-random repetitions in the sequence $$\sqrt{1}, \sqrt{12}, \sqrt{123}, \sqrt{1234}, \sqrt{12345}$$ as those only appear in alternating positions. —David Eppstein (talk) 05:41, 12 July 2024 (UTC)


 * That property looks more like clutter than a feature of interest, and the given source doesn't make a case for it. XOR&#39;easter (talk) 19:19, 12 July 2024 (UTC)
 * I found it interesting within its class of numbers. Do what you want you with it, I'm done fighting irrationally over things here. Radlrb (talk) 01:16, 13 July 2024 (UTC)
 * The reason I kept it is, because the first two strings are 33 and 00 that repeat in base ten. While yes, this property in these numbers happen to be of more import for odd-numbered square of digits, nonetheless this is the earliest appearance within this class of numbers, regardless of whether the chance is more than 1/3 for any number (i.e., within its class it is the first, and therefore the first within its class to fall under the greater probability within all classes of numbers). Inverting the question of "probability", then "what is the probability that any of these classes of numbers will not be inline with the tendency to have repdigits in the fractional part, within fractional powers of a number" and then move on to ask, "if it is outside the boundary of expectation, how many of these are also outside the line of expectation", and if it continues to fall out of line, then there is likely interesting mathematical behavior that can be outlined in formulaic fashion (if not, the converse is likely true, unless behavior is seen much later on in the sequence). Radlrb (talk) 02:47, 13 July 2024 (UTC)
 * "Out of line" would be on when these digits appear, and if their appearance follows some sort of behavior (as well as on how many repeat, which is already known to show increments), and so forth. In other words, appearing earlier on or further out for the first time in the square root of a mock-rational number, has significance if these are to be taken together as a group, and tell a story-line. Radlrb (talk) 02:51, 13 July 2024 (UTC)
 * This being said, you both already know this, so this is half-trolling or something : ). (55:38:25) Radlrb (talk) 02:56, 13 July 2024 (UTC)
 * And if we are going to be entirely clear, how this: "Because it is not divisible by 4, 1234 is the first number in these sequences that is not divisible by its final digit" is any more a "relevant property" with your same reasoning (other than "substantiated by a source"), then there is not enough fair critical reasoning going on (the amount of integers not divisible by their final digit in a given base is enormous, right? *base ten if it ends in 0, 2, 4, 6, 8, or 5 aside from 5 will be divisible by 2 or 5 alone or one of its multiples; etc. Radlrb (talk)* 04:29, 13 July 2024 (UTC)) I.e., a type of WP:Cherrypicking. My point (if it isn't clear) is that your contribution, and mine, are both worthwhile. (talk) Radlrb 04:14, 13 July 2024 (UTC)
 * Base 10 divisibility: (no divisibility by 0, all ending in 1 are divisible by 1, all in ending in 2 are divisible by 2); 3 if the sum of all digits of that number is divisible by 3, 4 if its last two digits are divisible by 4, 8 if its last three digits are divisible by 8, etc; divisible by 5 if ending in 0 or 5, 6 if it is divisible already by 2 or 3, and therefore if the digit sum of the number is a multiple of 3; for 7 taking twice the unit digit of the given number and subtracting the remaining part of the given number needs to be 7 or a multiple of 7 (or 0). 9 is the simplest, in some senses: if the digit sum of the number is divisible by 9, then the number is divisible by 9. So, divisibility of a number by its final digit is for the most part "predictable" and not exceptional, relative to base-specific divisibility rules, and aside from enormous numbers whose very digit computations becomes difficult for, and of course, for numbers that happen to be prime (and therefore, odd-looking), which can "appear" to make more sense digit-wise relative to given ranges in different bases (and, therefore an important clue in describing them). Radlrb (talk) 04:57, 13 July 2024 (UTC)
 * Radlrb please stop edit-warring to add your junk WP:SYNTH non-interesting property to this article. It should be removed. Despite most of this conversation being dominated by your walls of text replying to yourself I see no other supporters of this content. —David Eppstein (talk) 23:27, 13 July 2024 (UTC)
 * I'm not replying to myself, I am adding context to my own points (that is extremely rude of you to even say; so why even bother collaborating with you when you lack respectful scholarship here). The support I have comes in the form of all the number pages I have written and published on where all of the editors watching and vetting the information have let it stand. It's called silent support, something you are not aware of it seems. I don't blame hold anything against them for not speaking up (they don't necessarily need to), usually people who push interesting points are deemed uninteresting by those whose time has long passed, and stick to old dysfunctional archaic ideas. Radlrb (talk) 00:12, 14 July 2024 (UTC)
 * Interesting would be to see you respond to some of my points, rather than ignore them. It could give validity to your perspective, however you do not want to engage. In the light of true intellectual pursuit, you come heavily short, and all from substantial prejudice you still hold against me, and people of the like, who are willing to cross bludgeoned barriers of destruction that continue to exist today. But you're not the type to fight such heavy things. Radlrb (talk) 00:16, 14 July 2024 (UTC)
 * @David Eppstein, @Radlrb. I don't want to interfere your conversation here, but I think asking in WT:WPM is another option to give more perspective about this mock property. Dedhert.Jr (talk) 02:28, 15 July 2024 (UTC)