Quote: "Um, I think you missed the point.
The proof was invalid, that was what I was trying to show - just because you derive something that is true from an assumption, that doesn't mean the original assumption was true."
What I am about to tell you, will have to be clarified with your Math teacher, since we now need an authority that has to confirm who is right and who is wrong.
And I hope you don't consider my answering back to you as non-acceptance of math criticism on my part.
So...
Every proposed math theorem IS an assumption.
When you use a tautology or contradiction to prove that assumption you are said to have PROVED the theorem, which is no longer an assumption but a mathematically accurate statement.
And in the diagram, those 2 red arrows...
If you hadn't put those arrows there I would have wondered how the two b^2 "cancel out". I may be in first grade but please don't insult my intelligence to this extent
Another false statement you made
"c^2 = c^2 , which is true for all c"
Consider the complex plane.
For complex numbers
a = i
b = 1
we would have a right angled triangle with the vertex of the right angle at the origin of the complex plane.
a^2 + b^2
= i^2 + 1^2
= -1 + 1
= 0
We have shown that in the complex plane an example of a right angled triangle whose third side c = 0
This does not satisfy the Pythogoras constraint that a^2 + b^2 = c^2
Therefore, an accurate statement on your part would have been
"c^2 = c^2 , which is true for all Real numbers c"
I have not seen you defend any of the flaws that I have pointed out in your arguments. In which case how can I take any of your mathematical criticisms seriously. I wonder who is the one who is not open to mathematical criticism.
