## JSH: Lying about the distributive property

What makes this story even more dramatic though, especially in terms of the fraud involved, is that posters in fighting against my research are willing to lie about the distributive property--and they get away with it.

I can state the argument simply enough.

The distributive property simply enough says that if you multiply a group you multiply the elements within that group:

a*(b + c) = a*b + a*c

and there is no reason not to use functions so you may have

a*(f(x) + b) = a*f(x) + a*b

and here is where it gets really bizarre, as my position that the value of the function has no impact on the distributive property is now key, so I say that if at x=0, f(x)=0, then that is as valid a point as any other AS THE VALUE OF THE FUNCTION DOES NOT MATTER to the operation of the distributive property.

Now let's make a more complicated example:

7*(a + b)*(c + d) = (7*a + 7*b)*(c + d)

where it's still just the distributive property, but with more stuff, and now, like before, I'm going to put in functions, but then I have to be more careful than before:

7*(h(x) + b)*(c + d) = (f(x) + 7*b)*(g(x) + d)

because one of the functions just swallowed the 7 so that it is now invisible.

How can a function do that? Easy. It's a function, so it can be

f(x) = 7*h(x)

so the function swallowing the visibility of the 7 is not a big deal, but maybe though, it didn't so I add the rule that at x=0, f(x)=0 and g(x) = 0, so that I can SEE what is going on at a particular value.

If you had some other convenient value, that would be ok as well.

7*(h(0) + b)*(c + d) = (0 + 7*b)*(0 + d)

and it's clear that the 7 multiplied through like with

7*(a + b)*(c + d) = (7*a + 7*b)*(c + d)

while the functions just make things a little more complicated to verify, but not impossible.

Now then, by the logical point that the value of the function does not change the distributive property, I know what happened for ANY x, but posters in fighting this argument have proclaimed x=0 to be a "special case", defying the reality of how the distributive property operates.

I've explained, and explained, and explained so that the best conclusion is that posters lie about this argument.

Otherwise they can't understand the basic principle that the value of the function does not change the distributive property, which is a major stretch.

Why is it such a big deal?

Because once the principle is established, I can get some complicated functions that show a problem with the ring of algebraic integers.

Posters in defying what is mathematically correct are just slashing at what they can, and in this case, that means questioning the distributive property, and then claiming they are not doing so, while they claim x=0 is a special case, but if I push them on the point that the value of functions does not affect the distributive property, they
claim they don't disagree!

It's a case of where the lies just keep coming and it shows you how to defy a mathematical proof.

Just claim it's wrong, keep claiming it's wrong, and get enough people to claim it's wrong so that no one believes that it's correct.

And doing that you can block acceptance of mathematical proof.

These people are undermining the discipline of mathematics by showing its true fragility.

It has few defenses against dedicated group lying about mathematical arguments.

I mean, come on! The distributive property! How could people get away with lying about that?

But they have now, for years.