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July 30th, 2012, 11:11 PM  #1 
Newbie Joined: Jul 2012 Posts: 1 Thanks: 0  Understanding of the word "within" as used in math
I need a clear understanding of the word "within" with regards to translation in math. Like if I say integers of X is within the interval of 5 and 10. Does this mean: [5,10], or does it mean (5,10)?? The reason I ask this is because in the English language if I say: "You have within 24 hours to complete the tasks I have given you"; means that I have up to the 24th hour exactly to complete the tasks which means equal to the 24th hour or less, which to me translates to less than or equal to. Or if I have a machined part that must be within .01 mm then that means if it is 5 mm then it can be equal to 5.01 mm or less, but not less than 4.99 mm. So it can equal either of those extremes or be greater/less than. So I suppose the word within means less than or equal to? 
July 31st, 2012, 03:45 AM  #2 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Understanding of the word "within" as used in math
X within [5, 10]: The meaning is 5 < X < 10 The notation we use instead of writing "within" is Am I correct? Anyone please confirm . . . 
July 31st, 2012, 04:09 AM  #3  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: Understanding of the word "within" as used in math
In those terms, I think "within" can be ambiguous. I'd like to think that the intended meaning of the word "within" would be clear from the context, especially in mathematical writing. The definition I read in an online dictionary includes the edge of the domain specified: Quote:
To avoid ambiguity, use "in (0, 5)" or "in [0, 5]". I think this problem was probably the motivation for interval notation.  

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