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Title: (71-1)(71+1) = 71 Post by Grimbal on Jul 31st, 2004, 11:44am Here is an equation: (71-1)(71+1) = 71 The astute reader will notice it is not true. How can you make it a valid identity by adding (a) a single dot or (b) two dots or (c) a single straight line. Notes 1. For this problem, the 1 is a straight line, the 7 are 2 straight lines. 2. I want an IDENTITY. Adding / on = is not an option. [edit: change equation to identity] |
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Title: Re: (71-1)(71+1) = 71 Post by honkyboy on Jul 31st, 2004, 4:06pm for a single dot (a) [hide](71-1)(71+1)=7! A redundant dot could be added for two (not the intended answer I'm sure) (71-1).(71+1)=7![/hide] |
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Title: Re: (71-1)(71+1) = 71 Post by Grimbal on Jul 31st, 2004, 4:26pm So fast? Too bad. Even though I asked only one option, and this was the intended slution, on another forum we foud a solution for all 3 cases. So keep searching. |
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Title: Re: (71-1)(71+1) = 71 Post by Sir Col on Aug 1st, 2004, 3:55am If we don't have to state the base (4969), we could write (71-1)(71+1)[equiv]71? ::) It may just be semantics, but 3+4=7 is an identity, not an equation. An identity is true for all values, whereas an equation must contain a variable and is true for some, or none, of the values. For example, x=3, is an equation, because x need not always be 3; 3x+4x=7x is an identity, because it is true for all values of x. So how about the equation... [hide](71-L)(71+1)=71[/hide]? |
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Title: Re: (71-1)(71+1) = 71 Post by Grimbal on Aug 1st, 2004, 7:30am OK, ok, :( I want an identity, then. |
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Title: Re: (71-1)(71+1) = 71 Post by Sir Col on Aug 1st, 2004, 8:00am Sorry, I wasn't criticising. I realised my "answer" wasn't what you were after, but I've been working on the single line part and I am still having difficulties. I don't suppose you would accept an inequality either... (71-1)(71+1)[ge]71? :P |
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Title: Re: (71-1)(71+1) = 71 Post by Grimbal on Aug 1st, 2004, 2:15pm EQUALITY! That is what I meant by equation. So, no inequality either. |
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Title: Re: (71-1)(71+1) = 71 Post by Icarus on Aug 3rd, 2004, 9:32pm on 08/01/04 at 03:55:34, Sir Col wrote:
What? By the definitions I've always used, an equation is a statement of the form "A = B", where A and B are any valid expressions. 3+4=7 most certainly IS an equation, as is 3+4=89. The latter is false, but it is still an equation. There is no requirement that a variable be present. All that is required is that the statement equate two things. |
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Title: Re: (71-1)(71+1) = 71 Post by towr on Aug 4th, 2004, 12:21am Quote:
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Title: Re: (71-1)(71+1) = 71 Post by Sir Col on Aug 4th, 2004, 3:25am I got all excited when I saw that someone had posted here, thinking they had found a solution to Grimbal's last question. We've been down this road before, but... ;) Quote:
However, I checked in my (Collins) Mathematical Dictionary and it makes an interesting distinction... Quote:
In light of this, I concede that my original objection was a little pedantic. However, I've learned something new; and I don't mean that I am pedantic. (I already knew that!) :P |
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Title: Re: (71-1)(71+1) = 71 Post by honkyboy on Aug 4th, 2004, 11:17am I am stumped on the single straight line. How about this solution for four dots:[hide](71-1)::(71+1)=71[/hide] |
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Title: Re: (71-1)(71+1) = 71 Post by Grimbal on Aug 4th, 2004, 12:24pm A hint: ->[hide]The 2-dot solution is most likely to be found by a physicist... The straight-line one more by ... well ... a typographer. [/hide]<- |
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Title: Re: (71-1)(71+1) = 71 Post by Leonid Broukhis on Aug 4th, 2004, 7:32pm on 08/04/04 at 11:17:41, honkyboy wrote:
I am not familiar with this notation. What do 4 dots mean? A missing element of a sequence? |
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Title: Re: (71-1)(71+1) = 71 Post by Leonid Broukhis on Aug 4th, 2004, 7:33pm Grimbal, are you implying an [hide]overbar[/hide]? |
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Title: Re: (71-1)(71+1) = 71 Post by honkyboy on Aug 4th, 2004, 7:37pm Four dot is for arithmetic mean. 4::6=5. the average of four and six is five. |
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Title: Re: (71-1)(71+1) = 71 Post by Grimbal on Aug 14th, 2004, 4:41pm Ok, here are my answers. (a) [hide](71-1)(71+1) = 7![/hide] (b) [hide]put a dot over the first 1 and over the second 71. A dot is a derivation relative to time d/dt. For constants, it is zero.[/hide] (c) [hide](71 or (71-1 |
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