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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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