TI-83/84 sets of numbers/set theory

  • #1
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Main Question or Discussion Point

Here's what I want to do on the calculator.

1) Input sets of numbers, for example 3,6,9... in any notation, for example {3,6,9,infinity} or {x|x/3 >= 1 >= infinity}

2) use set theory (not now, but when I get into pre-cal/college.)
 

Answers and Replies

  • #2
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Hmm, making a program to parse set theoretical operations could be a rather daunting task. It would be useful, but also keep in mind that this series of graphing calculators has some notable limitations including the small quantity of RAM (and memory in general). Still, to take on the task, you will first need to figure out which language will be best for the task. Your options are (mainly) TI-BASIC, Assembly, or Axe. TI-BASIC might be the easiest to implement, but is by no means an efficient language. Axe and Assembly, however, are probably not a good option for anybody not already knowledgeable of the z80.

Your first hurdle will be the symbols. While there is the ASCII character for |, you will need to use some assembly program to access the character. For example, Xtra is a good program for accessing these miscellaneous characters. Next, the infinity symbol is not even in the ASCII set for the small or large fonts. This will be very challenging and may require you to create your own font or user interface altogether. There are several other tools that will allow you to do this, but the program will start to get cumbersome and large.

Your next hurdle will be in pattern recognition. If we feed the list {1,3,9,27,...} to the parser, we will want it to figure out the pattern, especially if we wanted to pass something like "{1,3,9,27,...} or {1,9,81,729,...}" using set OR logic. The coolest problem is that literally any number can follow that ellipses. I have written programs and algorithms to generate general formulas with infinitely many solutions, so the proof is available. The biggest problem, though, is that pattern recognition is best suited for artificial neural networks (ANNs) or parallel processing. While we could emulate simple ANNs, it would be excruciatingly slow and the memory requirements could start to turn massive. Remember, a floppy disc has 1.44 MB of memory which is about 58 times as much as the calculator's RAM, without programs or anything else installed. We would have to force user input for parsing anything but the simplest patterns to take advantage of our neural network (brains).

Then the rest is easy. Just define the rules for set logic (simple enough) and you have a program!
 

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