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June 22nd, 2015, 09:12 PM  #1 
Newbie Joined: Jun 2015 From: United States Posts: 5 Thanks: 0  New Math Symbol/Use?
So, I had an idea for new mathy stuff. It could be confused with addition, but it's not addition. What if you wanted to find a certain character in a string? I'll start off using ~ as the new math symbol I want to create, since I can't make my own and post it into the email (NOTE: THAT IS NOT THE MATH SYMBOL. I AM ONLY USING IT BECAUSE I CAN'T MAKE MY OWN!). So let's say my string of characters is 02468 and my x value is 3. x~02468 is the equation. Since my x is 3, we're going to use VERY basic substitution. 3~02468 is now the equation. Now, count over 3 spots in the equation. What's your answer? 4 is your answer, since it is x (which is 3) spaces over in the string value, which is 02468. :D Understand? Good. Now, what if I wanted to do this math, but start counting over at a certain spot in the equation? You' d have to input the number you want to start on in somehow. Okay, we're keeping the string the same: 02468. What if I wanted to count over x spaces, but start counting from the 2 instead of the 0? Oh, and x is 3 still. Well, here's the equation to do that: 2(3~02468). The two in front means start at the 2. The 3~ means count over three, and the 02468 is the string value. you count it over in. So what's your answer? If you said 8, you're right!! :D For the final part of this, what happens if you want to start counting from a certain number, but there are two of that same number in the equation? Well, you'd have to show which number to start counting from somehow. Our new string is: 123456478901. Our new x is: 5. Well, there are two fours in the string value! What will we do?! We'll have to determine which four to start from. This is what the equation would end up looking like: 1(4(5~123456478901)). Don't worry  it's not as bad as it seems. The (4 means that we start at the four, but which four? That's what the 1(4 is for. It means that we're going to start at the first 4 of the string, starting on the left (like you read math anyway). the 5~ tells us we're going to go over 5. What's 5 over from the first 4 in the string 123456478901? If you said 8, you're a pro at this! If now, try rereading what I wrote, and seeing if you can understand! :D Now that I've explained it all, it's time to do one problem on your own! What's 2(4(5~123456478901))? Send me your answers! And good luck! Anyway, this was the new math symbol I thought should be added to the system. It's REALLY easy to add in onto other math (For example, 1(2~012345)*3(5/2.5) would be 18), and it can be helpful at times too, especially when coding with numerically saved string data! And again, ~ won't be the symbol used for it. But I couldn't make a new one and post it on here, could I? xD Anyway, tell me what you think about it, and if you have any questions, ask! POSSIBLE QUESTIONS AND THEIR ANSWERS: 1) Q: What if the number you're starting on isn't in the equation? A: Well, then it's an impossible equation, and your answer should be No Solution. Just like regular math, there is always a way to have No Solution. For instance, 2x + 3 = 2x + 7 has no solution. Don't believe me, try it yourself! 2) Q: What if the equation says start on the second number, but there's only one of that number in the string? Would you just add that number onto the end of the string? A: NO WAY! You NEVER edit the string! That's like changing the value of x in an equation to make it easier on you! NEVER do that. Ever. The answer for this would be no solution as well. :) Thanks so much for reading all of this! Bye :D Last edited by Aboot4; June 22nd, 2015 at 09:12 PM. Reason: Smilies messed some things up. 
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 $2\sim278$ 
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 145~123456478901

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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