Math III

 

Born Free

Stay free
Where no walls divide you
You're free as a roaring tide
So there's no need to hide

Is division the opposite of being free?

Engineers such as myself may not care about the difference between approaching and being. We primarily care about close enough. But we understand that there is a difference. Division by infinity approaches zero, but it is NOT zero. A mathematician and a physicist would give different answers. The limit of a constant k divided by x, k/x,  as it approaches zero is undefined according to a mathematician, because if k is zero, then k/0 is undefined. If k is equal to zero, a physicist would  say 0/0 is 1 because the formula k/x approaches 1 as x approaches zero from the positive side. However if it were approached beginning from negative infinity, them its limit would be -1. So at 0 there is a discontinuity, but there is also a paradox because the limit is both -1 and 1.  Engineers like me don’t generally deal with negative numbers, and we have no dog in this fight, but work it out guys please. Discontinuities, abrupt changes in the slope of an equation, that we can handle. Paradoxes, contradictory values at the same value, typically indicate that a deeper truth is not yet understood. The fact that this involves division might be significant

As mathematicians and binary machine language computer programmers can tell you, multiplication is easy, division is hard. Multiplication of a by b, where a is the multiplicand and b is the multiplier, is the product ab. To get that product, you add the multiplicand to itself multiplier times. So multiplication and addition are easily linked. Also multiplication does not involve a change of case. If a and b are both integers then their product, ab, will also be an integer.

Division is not linked to subtraction in the same manner. If multiplication is just repeated addition, division is NOT repeated subtraction. Also division involves a change of case. The division of two integers will result in a rational number. It is even worse for roots. The root of an integer or a rational number can be an irrational number. Multiplication, or raising a number to a power, is a series of additions with no change of case. Division, or taking a root, is not a series of subtractions and it involves a change of case. The biblical injunction is “Be Fruitful and Multiply.”  “Divide and conquer” was said by Julius Caesar. I knew that there was a problem understanding that whole Render onto Caesar and God thing, but those who promote dividing us have at least made it clear on which side they are.