User blog:Nayuta Ito/Introduction To Bashicu Matrix System

Because Bashicu Matrix System is very difficult, so I will explain it.

Definitions of notations
Bashicu Matrix looks like this: (0,0)(1,1)(2,2)(3,3)(3,2)[8] Generally, there are finite pairs of brackets, which have finite whole numbers, followed by a number in square brackets.

Definitions of words
As for $$A = (a_0,a_1,...,a_m), B = (b_0,b_1,...,b_m), D=\{ 0,1,...,m \}$$,
 * The length of a sequence is the number of pairs of brackets.
 * The matrix above has the length of 5.
 * A sequence which has the length of 1 (or have one pair of brackets) is called the element of the sequence.
 * S is an sequence.
 * Z is (0,0,...,0), which has one or more zeros.
 * f(n) is n squared. (You can change this rule, but it's considered as a variant)
 * A+B is connection of sequence.
 * For example, (0,0)(1,1)+(2,2)(3,3)=(0,0)(1,1)(2,2)(3,3)
 * how to compare elements:

$$A < B \Leftrightarrow \forall i \in D ((a_iB$$, neither.

Here are simpler words: Compare A and B from the left to the light until you find a zero in B. If numbers from A is always bigger, $$A>B$$. If numbers from B is always bigger, $$A<B$$. If neither, neither is bigger. (If you find zero in B at the first number, B is bigger.)

Examples: I will use N for neither. (1,0)<(2,1) //compare 1,2 and 0,1 (0,2)<(1,0) //compare 0,1 because second number in B is zero (5,9)<(0,32) //first zero in B makes bigger than anything (0,2)N(2,1) //because 0 1 (1,3,0)<(2,0,0) //compare only 1,2 (1,3,0)N(2,2,0) //you also have to compare 3,2 (1,3,0)<(2,4,0) //because 1<2 and 3<4 (1,3,100,googol)<(2,4,0,googolplex) //do not compare after the first zero in B

How to calculate

 * Rule 1. [n]=n
 * It means that if there are no brackets, the number in the square brackets is the answer.
 * Rule 2. S Z[n]=S[f(n)]
 * It means that if the last bracket contain only zeroes, remove it and change n into [n].

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(below is the most important and difficult part)

Take free examples until you understand!
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