Lesson 7:
Numbers

Dzam, tpam, gam, pham, phtam, spam, pam, tsham, dam, bdam, tsam, ppam, ttam

Zero, one, two, three, four, five, six, seven, eight, nine, ten, hundred, thousand

Phtn'rmzh phtam zhymph phwphs n'lay spyayp. Phtn'rmzh tta zhymph phwphs n'lay spyayp

I saw four fish in the river. I saw about a thousand in the river.

Mathematical Operators

Many mathematical operators are essential in the use of everyday numbers. Mathematical operators are identified by their vowels: le. Mathematical operators come after the numbers they operate on. The ones essential to everyday numbers are "ttle", "tlen", "tle", and "gdle" which mean "plus", "times", "divided by", and "to the power of" respectively. These are illustrated in the examples below.

Phtam gam ttle, phtam gam tlen, phtam gam tle, phtam gam gdle

Four plus two, four times two, four divided by two, four to the power of two

Compound Numbers

Why are mathematical operators essential? Because one can't say a number any larger than 10 without them, with the exceptions of 100 and 1000. All the numbers in a mathematical operation must have the same strength.

When adding number together to form bigger numbers, the larger numbers usually come first.

Tsam pam ttle

Sixteen

When multiplying to obtain larger numbers, multiples of ten usually follow the multiplier.

Pam tsam tlen

Sixty

In order to obtain powers of ten greater than one thousand, raise either 1000 to the desired power.

Ttam gam gdle

One million

Real life sometimes requires numbers more complicated than given previously. Each compound number may become a number in another mathematical operation.

Ga tsa tlen da ttle tta pha gdle tlen

About twenty-eight thousand million

Or even scarier:

Gam tsam tlen dam ttle ttam pham gdle tlen pham ppam tlen phtam tsam tlen ttle spam ttle ttam gam gdle tlen ttle gam ppam tlen tsham tsam tlen ttle phtam ttle ttam tlen ttle tsam bdam ttle ttle

Twenty-eight thousand million, three-hundred forty-five million, two-hundred seventy-four thousand, nineteen

Fractions

Fractions are easy, relatively. They are expressed as divisions.

Tpa pha tle, pam tsam tpam ttle tle

One third, six elevenths

Decimals on the other hand are evil. They are expressed as the sum of multiples of powers of 1/10. You can use 1/100 and 1/1000, but after 3 decimal places it's necessary to use 1/10^4, 1/10^5, etc.

Pa tsa tlen tsha ttle bda tsa tle ttle phta ppa tle ttle spa tta tle ttle da tsa phta gdle tle ttle

Sixty-seven decimal nine four five eight

Other Bases

Due to the way Qtwyqp Qly expresses compound numbers, it's not really much harder to say numbers in number systems with bases less than ten. One could even use bases above ten if he didn't mind some of his digits being expressed as three or more words.

gam pham gdle gam gam gdle ttle tpam ttle,
tsham dam tlen phta ttle,
tsam spam ttle tsam pam ttle tlen tsam phtam ttle ttle

1101 (binary), 74 (octal), FE (hexidecimal)

Derivatives from Cardinals

Ordinals

Ordinals are the number ending in "th" (or "st", "nd", or "rd") in English. In Qtwyqp Qly, ordinals are derived from the corresponding cardinal simply by changing the a to e. In compound numbers, every cardinal must be changed to an ordinal. These number function as adjectives obeying all the same rules that cardinals do. The only difference is meaning: ordinals indicate the rank of a noun in a series.

Qn'ymqq phem n'ya ttla qnyqq n'ya zzoy.

My son is my third child.

Adverbial Ordinals

These are still ordinals, but they function as adverbs instead of as adjectives. They are derived from the cardinals by changing a to we.

Loym nloy dyoy tswem. Phthymq n'lay bnyaytq gwem.

He finished tenth. Secondly, I built a house.

Number of Occurances

These numbers translate the English "once, twice, thrice," etc. They are derived from the cardinals by changing a to wo. They also act as adverbs.

N'lay byaymq phtwom. Ttlwn!

I've been married four times. No more!

More Mathematical Nightmares

More on Mathematical Operators

As stated earlier, mathematical operators are recognized by le. About the only important mathematical operator that wasn't introduced earlier was "ttlen", which means "minus". However, I didn't explain negation. An operator may be negated by adding an n to the vowels. Mathematical operators are the only part of speech for which negation always causes a word to take the opposite meaning instead of a simple denial of its meaning. Thus we have "ttlen" (minus) from "ttle" (plus), "tlen" (times) from "tle" (divided by), and "gdlen" (logarithm base ... of ...) from "gdle" (to the power of). For those who would claim that the opposite of "to the power of" is "the ... root of ...": I disagree. The logarithm is the inverse function of the exponetial function. In order to get roots (such as square roots), you must raise the number to a fractional power.

Phtam gam ttlen, gam phtam gdlen, phtam tpam gam tle gdle

Four minus two, log two of four, the square root of four

Negative Numbers

Negative numbers may be formed by subtracted the corresponding positive number from zero.

Dam, dzam dam ttlen

Eight, negative eight

pi & e

Here are a couple of very important mathematical constants:

bhzhamqh, gdam

pi, e

Complex Numbers

These numbers are the horror and confusion of algebra students everywhere, and trying to say them in Qtwyqp Qly makes them even worse. The imaginary constant must be expressed as the square root of negative one.

dzam tpam ttlen tpam gam tle gdle

i

Complex numbers are expressed as the sum of a real number and an imaginary number.

phtam bdam dzam tpam ttlen tpam gam tle gdle tlen ttle

Four plus nine i.

Relational Operators

Formation