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 September 12th, 2011, 05:04 AM #1 Member   Joined: Sep 2011 Posts: 97 Thanks: 0 prove the floor of two numbers is the same as.... let [] be a floor function For all real number x and all integers m, show that [x + m] = [x]+ m
 September 12th, 2011, 05:48 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond Re: prove the floor of two numbers is the same as.... [x + m] = [[x] + {x} + m] = [x] + m, where {x} denotes the fractional part of x, i.e. {x} = x - [x]. edit: I think that's right; the fractional part is defined to be positive or zero.
 September 12th, 2011, 03:53 PM #3 Member   Joined: Sep 2011 Posts: 97 Thanks: 0 Re: prove the floor of two numbers is the same as.... ?? so it's proven just like that? that simple?
 September 13th, 2011, 01:31 PM #4 Senior Member   Joined: Apr 2010 Posts: 215 Thanks: 0 Re: prove the floor of two numbers is the same as.... Not all real numbers have fractional parts right?
 September 13th, 2011, 01:53 PM #5 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond Re: prove the floor of two numbers is the same as.... Integers don't, unless you count 0/?. x is real.
 September 14th, 2011, 02:17 AM #6 Member   Joined: Sep 2011 Posts: 97 Thanks: 0 Re: prove the floor of two numbers is the same as.... so i think you guys need to help explain on how the answer of derived?
 September 14th, 2011, 02:42 AM #7 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: prove the floor of two numbers is the same as.... I think a little more argument is needed... First, if A is an integer and 0 ? B < 1, then [A+B] = [A] = A. Also, x = [x] + {x} where [x] is an integer and 0 ? {x} < 1. [x+m] = [[x]+{x} + m] = [[x]+m + {x}], and [x]+m is an integer, because an integer plus an integer is an integer. And 0 ? {x} < 1. Let A = [x]+m and B = {x} and compare with the first statement above. Therefore [x+m] = [[x]+m] = [x]+m.
 September 14th, 2011, 07:28 AM #8 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,950 Thanks: 1141 Math Focus: Elementary mathematics and beyond Re: prove the floor of two numbers is the same as....

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### prove that floor x m = floor x m

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