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#1 Re: This is Cool » Shaking The Foundations Of Mathematics. » 2012-07-21 20:31:34

Don Blazys wrote:

That is not true. I am not dividing by zero. In fact, I am doing exactly the opposite!

Don Blazys wrote:

Quoting MrButterman:

Your problem is at the third step. The fraction is equal to 0/0 and thus no longer equals the value in the second step.

At

, your equations contain the removable singularity which is so utterly trivial that we mathematicians refer to it as "cosmetic".
In this particular case, since
the expression
at
by definition .
Thus, in this particular case, that indeterminate form
, so at

By contrast, at

, my equation has a non-removable singularity which demonstrates that some axioms are not always true!

The third step (and beyond) is only valid as long as a = b. But you are applying it to cases where a =/= b!

#2 Re: This is Cool » 0.9999....(recurring) = 1? » 2012-07-18 11:44:06

Interesting how this thread got so long.

is a mathematical fact. The reason it is so difficult for people to understand may be due to confusion over the concept of infinity. Here are some different ways to think about it:
___________

1) pointed out above

___________

2)

is equivalent to
. But since the number of 0's are infinite, you never "reach" the 1; it is equivalent to 0!
___________

3) a popular proof

___________

#3 Re: This is Cool » Shaking The Foundations Of Mathematics. » 2012-07-18 11:28:31

Don Blazys wrote:

The "foundations of mathematics" are its axioms, which are defined as "self evident truths".
So, let's have some fun with them. Let's "shake" those foundations a little and see what happens!

Consider the "symmetric axiom of equality" which states that "if

, then
.

Well, if

where
,

and the properties of logarithms allow

where
,

then clearly, that so called "symmetric axiom of equality" is neither self evident, nor always true!

Don.

You are dividing by zero in your exponent, so there must be something wrong here

Your problem is at the third step. The fraction is equal to 0/0 and thus no longer equals the value in the second step.