# lesson 10: numbers

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you’ve made it to the end! i'm proud of how far you all have come. now it’s time for everyone’s favorite subject: math! (and if it's not your favorite, don't worry—i’ll try to make this as painless as possible)

seximal

firstly, fynotek uses a seximal (base 6) number system. if you know what that means, skip to the “numbers in fynotek” section (and if you're technical enough for that, note that all numbers in this lesson are in decimal unless otherwise specified). if not, let's learn!

in our standard number system, we have ten digits: 0 to 9. once we reach 9, we’ve run out of ways to express numbers with just one digit! so, we add another digit and write ten as “10”. after that, we continue counting up until we run out of digits again, and so on.

each digit in our system has a value that is a power of 10: for example, the number “1521” really means “1 × 10^3 + 5 × 10^2 + 2 × 10^1 + 1 × 10^0” (note that any number to the zeroth power is 1). “running out of digits” really means that we’ve reached the next power of 10, and that’s why we need a new digit!

in a seximal system, we only have six digits (0 to 5), and instead of using powers of 10, we use powers of 6. instead of ones, tens, and hundreds, we have ones, sixes, thirty-sixes, and so on! here is an example of how to write some numbers in seximal:

• 0: zero
• 1: one
• 2: two
• 3: three
• 4: four
• 5: five
• 10: six
• 11: seven
• 12: eight
• [we are going to skip some numbers to make this quicker]
• 20: twelve
• 30: eighteen
• 40: twenty-four
• 50: thirty
• 100: thirty-six

and so on. as another example, the seximal number “11013” really means “1 × 6^4 + 1 × 6^3 + 0 × 6^2 + 1 × 6^1 + 3 × 6^0”, which is the same as 1521 in decimal!

most of the numbers in this lesson will be in decimal. if they're not, i'll let you know :)

numbers in fynotek

since seximal has digits from 0 to 5, fynotek has number words for 0 to 5:

• 0: fui
• 1: ay
• 2: fo
• 3: us
• 4: nos
• 5: pur

to go higher than 5, we need to have words for powers of 6. fynotek does this with suffixes, which multiply one of the digits from above by a power of 6. here they are:

• × 6^1: po
• × 6^2: pura
• × 6^4: poña
• × 6^8: sola
• × 6^16: manta
• × 6^32: tauwa

to multiply by a power not on this list, attach suffixes together to add up to the number you want, with the smallest one first (for example, to multiply by 6^3, you would use the suffix popura, since 1 + 2 is 3, and 1 is smaller than 2).

now let’s start making numbers! go digit by digit, making the word for each one. note that if the digit is 0, you just skip it, and you never apply the power suffixes to fui.

let's do an example! the seximal number “5103” is 5 × 6^3 + 1 × 6^2 + 0 × 6^1 + 3 × 6^0. let’s break that down:

• 5 × 6^3: 5 is pur, and the suffix for 6^3 is popura (since 3 is 1 + 2), so this part is purpopura.
• 1 × 6^2: 1 is ay, and the suffix for 6^2 is pura, so this part is aypura.
• 0 × 6^1: we just skip zeroes.

3 × 6^0: this really just means “3”, which is us.

so, the seximal number “5103” is purpopura aypura us!

to talk about negatives, simply add ñy before the number. as an example, 5 is pur and -5 is ñy pur.

now for fractions! to invert a number, suffix yla to it (e.g. a half would be foyla). you can then add a numerator to it by placing the numerator after yla (e.g. three eighths (eight in seximal is “12”) is aypo foyla us, or “eight-little three”). you can use ay after yla (so you can also write one-half as foyla ay) if you want, but you are not required to.

to express an amount of something, use the number as a normal modifier. this means that if you can attach the number, do so! for example, to say “seven things” (seven is “11” in seximal), you would say unsoakaypo ay. note that you don't attach the ay to the aypo—they must remain separate! also, note that you use ak if the number of things is greater than 1 (i.e. you would say unsofui for zero things, and unsofoyla for half of a thing, but unsoakfo for two things).

some more examples:

• i have 5 books. - skafas hoksakapur.
• there are no computers. - ilynfui fuho.
• you ate three quarters of the food. - piina pionosyla os.*

*note that “os” is us in o ablaut; since it is not attached to anything, it must undergo ablaut.

finally, to talk about ordinal numbers (first, second, third, etc.) attach rea to the end of the number (i.e. “first” is ayrea, “second” is forea, etc.). as an example, “i have the seventh book” would be “skafas hoksaypo ayrea.”

alright! now let’s talk about how to make some equations.

equations

these are pretty simple, and the word order is the exact same as an english equation. when you write equations, do not conjugate anything.

here are the words used in equations:

• + ah
• − raim
• × nohu
• ÷ kisak
• = hao

here are some examples:

• 3 + 5 = 8: us ah pur hao aypo fo
• 6 ÷ 2 = 3: aypo kisak fo hao us
• 4 - 1 = 2 × 2: nos raim ay hao fo nohu fo

fynotek to english homework (currently broken)

english to fynotek homework (currently broken)

vocab: