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 June 22nd, 2015, 10:08 PM #2 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 This new symbol may turn out to be mostly redundant unless you are using the operation repeatedly. If it is a once off use, you are probably better off writing what you mean in words. Having said that, it may still be useful in certain circumstances, although I don't know what these might be at this point. I have some issues with the notation. There's nothing wrong with the symbol itself, but $2(3\sim02468 )$ could be confused with $2\times(3\sim02468 )$ maybe instead, use $2\{3\sim02468\}$ or $2[3\sim02468]$ as these brackets are used less often in simple arithmetic. For the next part, I have similar doubts. $1(4(5\sim123456478901))$ could be confused with $1\times4\times(5\sim123456478901)$. Instead, I would use $4_1\{5\sim123456478901\}$ Where $a_1\{b\sim s\}$ is written as $a\{b\sim s\}$ if there is only one appearance of $a$ in the string $s$.
 June 22nd, 2015, 10:20 PM #3 Math Team   Joined: Nov 2014 From: Australia Posts: 689 Thanks: 244 Can an algebraic expression be used in the place of the string? In other words, can a number be used as a string in this notation, or is there a technical difference between the two? E.g $3\sim(2x + 7)$ Also, how would one deal with this if the value of $2x +7$ happened to be one digit? Would the notation only be valid for those values where $2x + 7 \geq 100$? The last question I have is, if numbers as strings are allowed, how would one deal with negative strings? E.g $2\sim-278$
 June 23rd, 2015, 04:24 AM #4 Newbie   Joined: Jun 2015 From: United States Posts: 5 Thanks: 0 Yes, you can add algebraic expressions into it. And you're right about when I use ~ and when I use the (), but like I said, I didn't really know how to add in new symbols to use. :P I could do this: 2(6(2~123456654321))*3(4+2) and I'd get 72, since the answer of the first part is 4, and the answer of the second is 18. 18*4 is 72.
 June 23rd, 2015, 05:43 AM #5 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 I don't really like the notation a(b(c~d)) for a quaternary operation. Maybe (a~b~c~d)? Or better still, ~(a, b, c, d). You could also do something like ~$_{a,b}^c(d)$ if you want to emphasize that $a$ and $b$ go together and $d$ is what is being 'operated on'. If I understand correctly $b$ and $d$ are strings and $a$ and $c$ are positive integers. Last edited by CRGreathouse; June 23rd, 2015 at 05:58 AM.
 June 23rd, 2015, 06:54 AM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra I have two (rather negative) comments to make, so I'll start off with something more positive: you are free to make up any symbols and operations you like. So, to the more negative stuff. Mathematics deals with numbers, not strings. That is not to say that there is no mathematics in strings, but given a number (53, for example), that is not a string "5" followed by "3". The string is an artifact of the decimal representation of the number, not of the number itself. If you represent the number under a different system you get a different string. This severely limits the value of your symbol/operation to the extent that any symbol you come up with is unlikely to taken into wider use. This leads into the second point, which is that mathematical symbols are a matter of convention. There are variations in conventions around the world, but by and large, mathematicians stick to notation that is familiar to their readers. Mathematical writing is about communicating the mathematical meaning, not obscuring it in unfamiliar hieroglyphics. If you really want to introduce new notation that will be taken up widely, your best bet is to come up with a groundbreaking paper that makes justified and extensive use of your symbol. If the importance of the paper is great enough, and the notation is "good" enough, mathematicians that follow on from your work may use it. Otherwise, I reckon your chances are slim.
 June 23rd, 2015, 07:05 AM #7 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 I think that the operation is not even mathematical -- it's working on strings, not numbers, and it's not doing something like combinatorics on words.
 June 24th, 2015, 12:14 PM #8 Newbie   Joined: Jun 2015 From: United States Posts: 5 Thanks: 0 Maybe instead of square brackets, I could use |. It's not a letter or number, and it's hardly used in math. So 1|4|5~123456478901
 June 24th, 2015, 12:15 PM #9 Newbie   Joined: Jun 2015 From: United States Posts: 5 Thanks: 0 Plus, this is very useful when working with programming languages such as JavaScript. It's more of a tool than a math symbol, in my opinion.
 June 24th, 2015, 12:47 PM #10 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra JavaScript probably has some sort of string index function that does this anyway. Perl certainly does.

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