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What is arithmetic?
The fundamental theorem of arithmetic states that {n: n is an element of N > 1} (the set of natural numbers, or positive integers, except the number 1) can be represented uniquely apart from rearrangement as the product of one or more prime numbers (a positive integer that's divisible only by 1 and itself). This theorem is also called the unique factorization theorem and is a corollary to Euclid's first theorem, or Euclid's principle, which states that if p is a prime number and p/ab is given (a does not equal 0; b does not equal 0), then p is divisible by a or p is divisible by b.
Proof: First prove that every integer n > 1 can be written as a product of primes by using inductive reasoning. Let n = 2. Since 2 is prime, n is a product of primes. Suppose n > 2, and the above proposition is true for N < n. If n is prime, then n is a product of primes. If n is composite, then n = ab, where a < n and b < n. Therefore, a and b are products of primes. Hence, n = ab is also a product of primes. Since that has been established, we can now prove that such a product is unique (except for order). Suppose n = p sub1 * p sub2 * ... * p subk = q sub1 * q sub2 * ... * q subr, where the p's and q's are primes. If so, then p sub1 is divisible by (q sub1 * ... * q subr) by Euclid's first theorem. What is the relationship between p sub1 and one of the q's? If the r in q subr equals 1, then p sub1 = q sub1 since the only divisors of q are + or - 1 and + or - q and p > 1, making p = q. What about the other factors in the divisor? If p does not divide q, then the greatest common denominator of p and q is 1 since the only divisors of p are + or - 1 and + or - p. Thus there are integers m and n so that 1 = am + bn. Multiplying by q subr yieds q subr = amq subr + bnq subr. Since we are saying that p is divisible by q, let's say the q sub1 * q subr = cp. Then q subr = amq subr + bnq subr = amq subr + bcm = m(aq subr + bc). Therefore, p is divisible by q sub1 of q sub2 * ... * q subr. If p sub1 is divisible by q sub1, then p sub1 = q sub 1. If this does not work the first time, then repeat the argument until you find an equality. Therefore, one of the p's must equal one of the q's. In any case, rearrange the q's so that p sub1 = q sub1, then p sub1 * p sub2 * ... * p subk= p sub1 * q sub2 * ... * q subr and p sub2 * ... * p subk = q sub2 * ... * q subr, and so on. By the same argument, we can rearrange the remaining q's so that p sub2 = q sub2. Thus n can be expressed uniquely as a product of primes regardless of order, making the fundamental theorem of arithmetic true.
arithmetic - meme gif
arithmetic - video
Arithmetic - what is it?
A dog that walks on three legs and carries one.
I should have consulted with the arithmetic dog before ordering the metal for my project, he always remembers to carry the one.
What does "arithmetic" mean?
The activists' and liberals' notion that giving birth to children is racism against the planet simply due to the fact that humans breathe out carbon.
Liberals and climate activists who believe in carbon arithmetic should stop reproducing. I think having more children is a wonderful thing.
Arithmetic - what does it mean?
Easy if you know how to spell maths
Me: 1+1=69 ...mental arithmetic sir.
Teacher: F......Fuck off
Arithmetic - meaning
A descriptive term used to describe an extreme erection.
When Katrina was sucking my dick and it got harder than fucking chinese arithmetic.
Arithmetic - definition
A term describing anything that is very hard to do.
This term has been around for years.
That test was harder than Chinese arithmetic.
Arithmetic - slang
The mental process of estimating the respective weights of the other passengers in an elevator. Then comparing it to the maximum weight posted next to the fire inspection sign to see if its safe.
After that big fat guy and the kid in the wheel chair got on, I redid the Elevator Arithmetic and decided I was going to take the stairs.
Arithmetic
a·rith·me·tic n. uh-rith-muh-tik; adj. ar-ith-met-ik
noun, slang
a telephone number, generally of a young, attractive female.
Man 1: "Who's that?"
Man 2: "That's Susie."
Man 1: "Man, she's fine...I'm gonna need that arithmetic."
Arithmetic
Arithmetic is a form of Elementary school math.
2 + 2 = 4
5 + 5 = 10
Shahriar + cupcakes = heaven
I learned arithmetic in elementary school.