mersenneforum.org Exciting discovery - but not sure what it means!
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 2005-09-13, 03:13 #1 chopinbrain   3×7×79 Posts Exciting discovery - but not sure what it means! Hello! I should probably not be posting this, because I really think I am onto something. But I am not a mathematician, though I am a musical prodigy. Anyway, enough of the delay... This HAS to mean something, any ideas what? And has anyone tried this before... I "stacked" two well known irrational numbers on top of each other. For example 2.34653122224 4.21431245553 Then I compared the digits of the top and bottom numbers up to 100,000 + spaces and running. (I have a program I wrote calculating as we speak) Anyway, up to 100,000 digits not one of the top or bottom numbers match! In the example above 2 is top 4 bottom then 3 top 2 bottom then 4 top 1 bottom. Since the chances of two numbers randomnly matching are 1 in 10. This is odd. Any ideas what this could mean. I am a geek! But this is pretty exicitng if you ask me. ANDY Anyway, astonishingly NONE of the numbers match. They are all different
 2005-09-13, 03:31 #2 jinydu     Dec 2003 Hopefully Near M48 2×3×293 Posts That's not really all that surprising. It's not difficult to come up with two irrational numbers whose decimal expansions never match at any digit. Here's an example: 0.0001000010000001... (the 4th, 9th, 16th, 25th, etc. [i.e. all perfect squares except 1], decimal places are ones, the rest are zeroes) 0.0010000100000010... (the 3rd, 8th, 15th, 24th, etc. [i.e. all perfect squares except 1, then subtract one], decimal places are ones, the rest are zeroes Your claim that "the chances of two digits being the same are one in ten" is only correct if the irrational numbers themselves were chosen randomly. Furthermore, you show know that there is nothing mathematically special about base 10 decimal expansions anyway; the choice of base 10 has more to do with humans having 10 fingers than with any mathematical necessity. Last fiddled with by jinydu on 2005-09-13 at 03:38

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