MAIN WRITING PART 2

                  MAIN WRITING   PART 2


              Additional Sustaining Reasoning


  Due to a certain practical reason, the expression 0:0 is considered indeterminate (0:0 = ind). But, in conventional Mathematics, 0:0 is equal to an infinite quantity of numbers, including zero,* for zero multiplied by any number is supposed to result in zero (axb = c   so   c:a = b) or, in other words, zero would be contained in zero any quantity of times. Therefore, IN CONVENTIONAL MATHEMATICS, though 0:0 is usually considered indeterminate, 0:0 is equal to the set of all numbers (including zero). This must be kept in mind for the following.
   
  The "fraction" 0/0 is considered to be equal to the expression 0:0 (in general, a:b = a/b). It's considered that 0:0 is equal to an infinite quantity of numbers (including zero) and is equal to the set of all numbers. Because of that, without enough reflection, it's considered that 0/0 is an infinite quantity of numbers too, equal to the set of all numbers. 
   a) But, if we analyze 0/0 considering, wrongly, that zero multiplied by zero results in zero, we'll get to the WRONG conclusion that 0/0 is no number. 0/0 would equal empty set (absence of any numbers). So 0/0 would be opposite 0:0, which would equal the set of all numbers (including zero). In the general expression a/b, the denominator (b) is a number of equal parts that constitute a unit  (the whole b-parts constitutes a unit and is equal to it). One part (p) multiplied by b results in one. But if the denominator (b) is zero, what can a "part" (p) be equal to, if every number multiplied by zero is supposed to result in zero?  In this case, the "part" would be NO number  (p = empty set).  If a = 0 and b = 0 then a/b is 0/0. The number of "parts" which would constitute the number 0/0, which is the numerator (a), is zero then 0/0 WOULD BE equal to empty set multiplied by zero (pxa), which results in empty set.*** Therefore, if zero multiplied by zero resulted in zero, the expression 0:0 wouldn't be equal to the "fraction" 0/0 (0:0 different from 0/0), and a:b = a/b wouldn't be a general equality. 
   b) BUT if we consider that zero multiplied by zero results in every number except zero, 0:0 is equal to the "fraction" 0/0. The expression 0:0 is equal to every number except zero because the divisor zero multiplied by the quotient, which is every number of an infinite quantity of numbers of every value different from zero, results in the dividend zero (dxq = D   so   D:d = q)**. The "fraction" 0/0 is zero of zero "parts" that constitute a unit, "parts" (p) which are equal to zero because zero (p) multiplied by zero (b), resulting in every number except zero, does result in one (among an infinite quantity of numbers different from zero). So the "fraction" 0/0 is equal to zero multiplied by zero (pxa), which results in every number except zero. The expression 0:0 and the "fraction" 0/0 are both equal to the set of all numbers except zero. THEREFORE 0:0 = 0/0 .
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Read Main Writing Part 3-B
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*In the condition of being a particular set of times zero, 0:0 is equal to every number equal to that particular set. For example, in the particular condition of being a set of times zero whose value is 7, 0:0 is equal to 7.
                        a) IN CONVENTIONAL MATHEMATICS, 0:0 is equal to every number so, in general, it's equal to the set of all numbers.
** b) If 0x0 results in every number EXCEPT zero, 0:0 is equal to every number EXCEPT zero so, in general, it's equal to the set of all numbers EXCEPT zero.
*** The product of empty set multiplied by zero results in empty set because, there not being zero as a multiplicand, it's not possible to obtain any numbers different from zero as a product and, there not being any numbers different from zero as a multiplicand, it's not possible to obtain zero as a product. Therefore the multiplication empty set multiplied by zero does not result in any numbers; it results in empty set. BUT the reasoning with which we got to the FALSE conclusion that 0:0 was different to 0/0 is based on the false assumption that zero multiplied by zero results in zero so I'll prove that, even on that false assumption, empty set multiplied by zero would result in empty set too.
 I) In order that empty set multiplied by zero resulted in any number different from zero, the multiplicand should be zero (zero multiplied by zero is absence of absence). But:
                                                        a) this contradicts the assumption that zero multiplied by zero results in zero.
                                                        b) the multiplicand is empty set, absence of any numbers; there is no zero as the multiplicand.
So no number different from zero would be obtained.
 II) In order that empty set multiplied by zero resulted in zero, the multiplicand should be a number different from zero, with which the multiplication would be absence of HABER (absence of SOME?), or the multiplicand should be zero, wrongly considered by conventional Mathematics; numbers that there are not as the multiplicand for this is empty set. So zero would not be obtained either.
  Therefore, even on the false assumption that zero multiplied by zero results in zero, empty set multiplied by zero would not result in zero nor any numbers different from zero. Empty set multiplied by zero would result in empty set.
  Some people may not be satisfied with the part II of this reasoning. All right!! If you want, consider that empty set multiplied by zero results in zero. If zero multiplied by zero resulted in zero, 0/0, which would be equal to empty set multiplied by zero (pxa), would be equal to zero so, even in the case that empty set multiplied by zero resulted in zero, 0/0 would be different from 0:0, which, in conventional Mathematics, is equal to the set of all numbers.