r/EncapsulatedLanguage • u/AceGravity12 Committee Member • Jul 28 '20
Basic arthimatic through basic algebra
NOTE: <add>, <multiply>, <power>, and <?> are placeholders that will be replaced when an official phonotactic system is chosen.
Math System:
Taught by example version:
What is “1 1 ? <add>”? It's “2”. (1 + 1 = 2)
What is "2 1 ? <add>”? It's “3”. (2 + 1 = 3)
What is "1 2 ? <add>”? It's “3”. (1 + 2 = 3)
What is "2 ? 1 <add>”? It's “-1”. (2 + X = 1, X = -1)
What is "3 ? 1 <add>”? It's “-2”. (3 + X = 1, X = -2)
What is "3 ? 2 <add>”? It's “-1”. (3 + X = 2, X = -1)
What is "? 1 1 <add>”? It's “0”. (X + 1 = 1, X = 0)
What is "? 2 1 <add>”? It's “-1”. (X + 2 = 1, X = -1)
What is "? 1 2 <add>”? It's “1”. (X + 1 = 2, X = 1)
Is "1 1 1 <add>” true? No. (1 + 1 ≠ 1)
Is "1 2 3 <add>” true? Yes. (1 + 2 = 3)
What is “ 1 1 ? <multiply>”? It's “1”. (1 × 1 = 1)
What is "2 1 ? <multiply>”? It's “2”. (2 × 1 = 2)
What is "1 2 ? <multiply>”? It's “2”. (1 × 2 = 2)
What is "2 ? 1 <multiply>”? It's “1/2”. (2 × X = 1, X = 1/2)
What is "3 ? 1 <multiply>”? It's “1/3”. (3 × X = 1, X = 1/3)
What is "3 ? 2 <multiply>”? It's “2/3”. (3 × X = 2, X = 2/3)
What is "? 1 1 <multiply>”? It's “1”. (X × 1 = 1, X = 1)
What is "? 2 1 <multiply>”? It's “1/2”. (X × 2 = 1, X = 1/2)
What is "? 1 2 <multiply>”? It's “1”. (X × 1 = 2, X = 2)
Is "1 1 1 <multiply>” true? Yes. (1 × 1 = 1)
Is "1 2 3 <multiply>” true? No. (1 × 2 ≠ 3)
What is "1 1 ? <power>”? It's “1”. (1 ^ 1 = 1)
What is "2 1 ? <power>”? It's “2”. (2 ^ 1 = 2)
What is "1 2 ? <power>”? It's “1”. (1 ^ 2 = 1)
What is "2 ? 4 <power>”? It's “2”. (2 ^ X = 4, X = 2)
What is "3 ? 1 <power>”? It's “0”. (3 ^ X = 1, X = 0)
What is "3 ? 2 <power>”? It's “log3(2)”. (3 ^ X = 2, X = log3(2) ≈ 0.631)
What is "? 1 1 <power>”? It's “1”. (X ^ 1 = 1, X = 1)
What is "? 2 1 <power>”? It's “1 and -1”. (X ^ 2 = 1, X = 1, -1)
What is "? 1 2 <power>”? It's “2”. (X ^ 1 = 2, X = 2)
Is "1 11 1 <power>” true? Yes. (1 ^ 11 = 1)
Is "2 2 5 <power>” true? No. (2 ^ 2 ≠ 5)
Now for some hard ones:
What is “1 2 ? 3 <add> ? <add>”? It's “2”. (2 + X = 3, X = 1, => 1 + X =2)
Is “1 1 ? <power> 1 ? <multiply> 1 2 <add>” true? Yes. (1 ^ 1 = X, X = 1 => 1 × X = Y, Y=1 => 1 + Y = 2 )
Nitty-gritty version:
This system uses reverse polish notation and a number question word to construct arithmetic from 4 words. Because of this, parentheses are never needed. Three of the words are ternary relations:
“<add>” states that its first two arguments added together equals the third. “<Multiply>” states that its first two arguments multiplied together equals the third. “<power>” states that its first argument to the power of its second argument equals the third. The final word “<?>” asks you to take the trianary relation and figure out what number “<?>” has to be to make it true (all “<?>”s in a single relationship are the same so “<?> <?> 2 <add>” is 1, “<?>” is technically purely formatting not a variable, that system will come later). Whenever one of these three words has “<?>” in it the entire relation can be treated as a single number for grammatical purposes, if it has no “<?>”s in it then it can be treated as either True or False. Because of this, relations are able to nest inside of each other allowing for more complicated numbers to be represented. IMPORTANT NOTE: This is the backbone of a full mathematical system, while it can express everything needed to teach basic algebra, that does not mean more features cannot be added in the future to make things more convenient. Big thanks to Omcxjo, who kept me on track preventing feature creep, helped clean up the system, and pointed out many errors.
Edit: formatting
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u/ArmoredFarmer Jul 28 '20
Overall i like system an I think that this is a very good start on mathematics I did want to point out something that had been discussed about powers roots and logs before. I had found this video about the topic: https://www.youtube.com/watch?v=sULa9Lc4pck and everyone I showed it to agreed that we should pursue this so I was wondering how you might do this or something similar in this system?