intended for trained mathemematics
Theorem: to prove that every real number is the result of divisions of two integers
To prove this theorem, I will bring the term (one digit, two digit , three digit,... real numbers), they show how many digits beyond the natural (whole) numbers after the commas (points)
R = Z: (10 ^ x), x different from the number zero
b = {1,2,3,4,5,6,7,8,9} a = {0,1,2,3,4,5,6,7,8,9} possible values and a(b)
R-real numbers, Z-whole numbers
x = 1, Z : (10 ^ 1) = {Z,Z.b}
x = 2, Z: (10 ^ 2) = {Z, Z.b, Z.ab}
x = 3, Z : (10 ^ 3) = {Z, Z.b, Z.ab, Z.aab}
x = 4, Z : (10 ^ 4) = {Z, Z.b, Z.ab, Z.aab, Z.aaab}
x = 5, Z : (10 ^ 5) = {Z, Zb, Z.ab, Z.aab, Z.aaab, Z.aaaab}
....
when the value of x is infinite, as the results are all real numbers
This evidence proves that the real and rational numbers one and the same numbers to irrational numbers do not exist, set this theorem to their mathematics teachers, and this shows that the current mathematics is limited and that there are errors (this is one of the errors). All solutions are not shown because for this we need all the infinite states, but was given a sample (as well as natural (whole) numbers are not written all but given sample. You think differently from what you give in school.