0

Given a set of operations and a set of numbers and optionally other constraints, I want to know what the set of all mathematical expressions is called that have the same result.

For example, given the integers 1 to 6, the operation addition, and the additional constraints "at least one term is 1" and "maximum of 3 terms", the set of all possible expressions that result in 5 is:

1+1+3
1+2+2
1+3+1
1+4
2+1+2
2+2+1
3+1+1
4+1

Or for example, given the integers from 0 to 10, and the operations addition, subtraction, multiplication, and division, there are many (in fact, infinite) expressions that result in the number 7.

Here are some of them (but not all):

7
3+4
(2*4)-1
0+0+0+7
3+(8/2)
1*7
((6+9)/3)+2
(2*5)-(4-1)
((6*4)-3)/3
etc.

How do you call the full set of all possible expressions that, given a set of numbers, and operations and optionally other constraints, yield into the same result?

Xavi Montero
  • 103

1 Answers1

1

Equivalent expressions. This is what you call a set of expressions the are equal (in other words, share the same results).

Mrigank Tanirwar
  • 26
  • Really? Usually there are some permitted transformations, like commuting elements, so "1+3" and "3+1" are considered equivalent. But I don't know that I would consider "2*2" and "1+3" to be equivalent. – JonathanZ Nov 25 '23 at 19:06
  • According to the definition that I asked for, meaning that "they have the same result" it makes sense. I was not asking about the "meaning of the terms giving that result" but "all that share the result" no matter how it's created. Equivalent = Equi-Valent == Their value is equal.

    Of course, if we look at the "meaning of the semantincs on how the formula is constructed" 1+3 and 2*2 are "not the same meaning". But at the end "ther value is equal" so they are "equi-valent".

     – Xavi Montero Mar 06 '24 at 19:10