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#1 Re: This is Cool » Shaking The Foundations Of Mathematics. » 2012-07-21 20:31:34
That is not true. I am not dividing by zero. In fact, I am doing exactly the opposite!
Whoops, my bad haha
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 , your third step is clearly equal to your second step.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)
___________
3) a popular proof
___________
#3 Re: This is Cool » Shaking The Foundations Of Mathematics. » 2012-07-18 11:28:31
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.
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