Proof of the Pudding

Some have expressed scepticism over some of my thoughts about the relationship between infinity and zero in my previous blog post here.  In order to bolster my case let me offer the following supporting evidence:


A well known mathemaical lemma is that one can find the perpendicular to the equation of the line Y = aX + b (a and b are any numbers, including zero) by taking the negative reciprocal of the coefficient of X.  Thus the previous equation's perpendicular line's equation would be Y = -1/aX + c  (c is any number and c may or may not = b).

So, by definition we know that the Y-axis (equation X = 0) is perpendicular to the X-axis (equation Y = 0).  How then can one use the previous lemma to prove this?

Start by applying this lemma to the equation of the X-axis yielding:  Y = -1/0 X.  Since, as I have stated previously 1/0 = ∞, then this equation becomes Y = -∞ X.  Dividing both sides by -∞, yields -Y/∞ = X.  And since we also were taught in the previous blog post that 1/∞ = 0, then this equation becomes -0 = X or (-0 and 0 being the same),  X = 0, which is the equation for the perpendicular Y-axis.  Q.E.D.

The Sky’s the Limit

Most mathematicians agree that 1/0 = ∞ (infinity) and that 1/∞ = 0. However, this consensus breaks down when confronted with what 0/0 is … or what ∞/∞ is. I think that most mathematicians today would say that 0/0 = 0 and ∞/∞ = ∞. I disagree … and assert that both 0/0 = 1 and ∞/∞ = 1. Here are my rationales for this … derived from the use of limit theory (the basis for the Calculus):

1/1 = 1
0.1/0.1 = 1
0.01/0.01 = 1
0.001/0.001 =1
0.0001/0.0001 = 1
0.00001/0.00001 = 1
0.000001/0.000001 = 1
And so forth
Ergo:
0/0 =1

and

1/1 = 1
10/10 = 1
100/100 = 1
1,000/1,000 =1
10,000/10,000 = 1
100,000/100,000 = 1
1,000,000/1,000,000 = 1
And so forth
Ergo:
∞/∞ = 1

All I ask is that I (George W. Potts) be so acknowledged for these assertions in mathematics anthologies.