The most laughable equation of all time in mathematics: e^(iπ) = -1.

One who disagrees with mainstream opinion is not necessarily a crank.

A crank is first and foremost one who cannot be convinced in the face of overwhelming evidence.

JG: What does "sqrt remains distributive over multiplication when it is extended" even mean?

Crank Malum: It means you "assume"

JG: In mathematics, we do not "assume" anything.
It is a FACT. sqrt(axb) = sqrt(a) x sqrt(b)

Crank Malum: It is valid. That is only true for non-negative a and b.

JG: Correct.

Crank Malum: For negative a and b, it is not distributive.

JG: Contradiction!

sqrt(axb) = sqrt(a) x sqrt(b) is stated formally. In mathematics,
there are no tricks, only in magic. Nothing happens by accident.
Chuckle.

Crank Malum: It isn't formally so, it is again a mental thing to ease use.

{In mainstream mathematics, whenever you can't explain anything, just refer to it as a "mental thing to ease use" - much like one might use lubrication to make it easier hammering a steel nail in a brick wall?}

JG: From one who constantly blabbers about "formal systems", suddenly
formality is not so important. Malum, you should join a circus soon!

The most laughable part is this:
sqrt(-9) = sqrt(9 x -1) = 3 x sqrt(-1) = 3i

Crank Malum: Which is invalid cause you assume it is distributive. It does however result in correct.

JG: It's invalid but correct? Hmm. Much like your "formal system" ? Chuckle.

{In mainstream mathematics, claims do not have to be valid in order to be correct!}

JG: You can't even have 3i if the identity sqrt(axb) = sqrt(a) x sqrt(b) does not hold. LMAO.

Crank Malum: Actually you can.

{Have faith and you can move mountains? Chuckle.}

JG: No, you can't, because in mathematics we deal only with hard, cold facts and logic. There is no place for religion.

Crank Malum: Sqrt(-9), what complex number fits that? 3i. You don't need to do distributive only remember that 3i*3i=-9

JG: Ah! You can go one way, but not the other. Believe in i^2 = -1 but don't ever try to go the other way because that is a sin!

What this idiot is telling you is this:

i^2 = -1 is okay, but sqrt(i^2) = sqrt(-1) is not NOT okay.

They know that sqrt(-1) is an ill-formed idea, so try to stay away from it whenever possible.

This is the state of today's mainstream "mathematics". It's more a cult than a science of any sort.

[marcolivgo]

Hi, John!

I just saw a video at the MindYourDecisions channel. They claim the definite integral of -1^x in the (0, 1) interval is 2i / pi. In your opinion, what would be the correct answer? The video title is "A Surprising Answer!". Thank you.

[NewCalculus]

Before you mouth off your ignorance, please note that I understand complex number theory as well as the best there is:


What I am telling you is that I do not agree with it!

I have had the misfortune of teaching this nonsense in my A Level lessons.