April 3rd, 2012, 09:28 PM  #1 
Newbie Joined: Apr 2012 Posts: 2 Thanks: 0  Logic
Hi, I have this problem whereby I need to convert a sentence into a logic statement. It'd be great if I could get some feedback on where I am going wrong/right. The sentence to translate: Let if for every then . I have come up with two possible translations: 1. Let 2. Let I am leaning towards my first translation. What does everyone else think? Thanks. 
April 3rd, 2012, 09:38 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Logic
Yes, the first one is right. The second one says something else which happens to be correct: if x <= y + e for e > 0, then x <= y.

April 3rd, 2012, 09:46 PM  #3 
Newbie Joined: Apr 2012 Posts: 2 Thanks: 0  Re: Logic
Thank you so much CRGreathouse!

April 4th, 2012, 03:04 AM  #4  
Senior Member Joined: Apr 2010 Posts: 451 Thanks: 1  Re: Logic Quote:
Only a formal proof justifies the correctness of a formula ,since there are not rules in tranlating from words to symbols,you should know that. And formulas in mathematics are closed formulas,so technicaly speeking none of the formulaes of the OP are correct  
April 4th, 2012, 06:03 AM  #5  
Senior Member Joined: Apr 2010 Posts: 451 Thanks: 1  Re: Logic Quote:
Why should the 1st one be the correct one?  

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