Mathematics

Is Division by zero possible – Yes



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Division by zero is possible, especially 0/0 because 0*0=0 and 0-0=0 (Explained further in next paragraph), which appears to prove that 0/0=0. However, the fact that 0*x where x is any number also equals zero appears to violate the laws of mathematics. Many years ago a square root of a negative number was thought to be an impossibility, but the German mathematician Carl Friedrich Gauss provided a an explanation for imaginary numbers, that the square root of -1 is i. The other integers besides zero are a little harder. A subtraction method can be used to suggest that any integer when divided by zero will remain that integer. It also can be explained in words:  Any integer will remain itself when divided zero times, which is approximately what dividing by zero is.

Any division of an integer by any other integer with no remainder can be expressed as follows: subtracting the number in the denominator from the integer in the numerator the number of times the denominator divides the numerator if the remainder is zero, or subtracting the number of times the denominator divides the numerator minus the remainder will both always equal zero.  Here are some examples:   9/3=3, or 9-3-3-3=0 (3 subtracted from nine three times), 14/7=2, or 14-7-7=0, 25/4=6 with a remainder of 1, or 25-4-4-4-4-4-4-1=0. 

This means any integer divided by zero will be that integer itself using this method: 7/0=7, 100/0=100, 121232233/0=121232233. Checking, 7-0=7, 100-0=100, 121232233-0=121232233.  One drawback is the integer in the numerator has not been subtracted from the denominator any number of times because 0 is not zero times, although it does equal zero.    

This should be possible to improve mathematically much like imaginary numbers were an improvement to the old axiom that there cannot be a square root of a negative number because all squares are positive. The axiom that states that if a/b=c, then c*b=a does not work, however, because of course although we have 7/0=7, 7*0=0. However, subtracting zero from any number zero times equals that number. Examples are 7-0=7, 9-0=9, 10034-0=10034, etc. Dividing fractions and decimals by zero is analogous to dividing integers by zero. For example, ¾-0=3/4, 9/10-0=9/10, 0.8-0=0.8, 111/99-0=111/99, 2.35-0=2.35.

But the German mathematician Carl Friedrich Gauss (1777-1855) had the same problem with imaginary numbers. The problem was that he was trying to find the square root of negative numbers when the only square roots that were known were positive because the square root of a negative number appears to be impossible because a negative integer times a negative integer is a positive integer. And when a negative integer times a positive integer was attempted to get a negative integer two unequal integers were the result because of the change of sign (for example, -1 times +1 is -1, but -1 does not equal +1).

Gauss devised a graphical concept for imaginary numbers. One way to look at it is if the denominator is zero then we are dividing the numerator by nothing zero times. For example, if we start with 7 oranges and do not divide them by anything, then we are left with 7 oranges. Another way to get the concept of zero is the fact that the oranges could be any size. This will make 7 small oranges equal to 3 large oranges in weight, so if we are concerned with the weight we have 7 equal to 3. This could make any number equal to any other number physically. They are approximate numbers because it is too hard to measure, for example, anything infinitesimal or infinitely large. Numbers infinitely big or small cannot be measured even with the aid of a computer.



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