Just because my posts aren't in LaTeX implies tgat I am wrong? That is truly false logic.

I am not beating around the bush. I have directly stated in post #44. If you don't see it I can explain it in more detail or have somebody else explain it to you.

Neither of you have read my comment on cmowla's graphs.

Last edited by anonimnystefy (2012-07-27 18:56:32)

No, it just implies that I am on my phone. If I was on my computer like I am now, I would be glad to LaTeX anything that needs LaTeXing.

The two graphs aren't the same. The second one has singularities along the line x=y.

No it doesn't. Did you look at post #44? Can you comprehend it correctly?

anonimnystefy wrote:

Don Blazys wrote:

This is the flawed step. He turned an exponential with base a^3/b to an exponential of the form 1^(log_1(...)) (which is "against the rules") and then turned that into a fraction using logarithm rules.

This is the post I am talking about. It shows that you are wrong.

It is not an identity. It is an identity when a<>b.

The thread is reopened for posting.

It is flawed because you assumed in the begnning that a=b. The identity doesn't hold when a=b.

Quoting anonimnystefy:

The identity doesn't hold when a=b.

That's what I said in the opening post of this thread!

So, do we now agree that given the identity:

we can never let

or substitute

for

even though those so called "axioms of equality" say we can?

Don

Quoting anonimnystefy:

The axioms of equality do not say we can do that.

Of course they do! Take for instance the substitution axiom of equality which states that
if two quantities are equal, then one can be replaced by the other in any equality or expression.

Well, the two quantities

and

are indeed equal,
but if we try to replace 

with

in the identity

,

then we quickly find that it's quite impossible, because clearly, the above identity has thoroughly and irrevocably
negated the closely related symmetric axiom of equality which states that if

, then

.

Now, this is not the first time that a faulty axiom has been negated by a perfectly logical mathematical construct.
We must not forget that the negation of Euclids fifth axiom (parallel postulate) ultimately resulted in many vastly
superior "non-Euclidean" geometries, one of which even allowed Einstein to formulate his theories of relativity!

Don.

Quoting anonimnystefy:

The substitution cannot be done because the of the restrictions that the lofarithms pose.

You see folks, that so called "substitution axiom of equality",
which states that we can always and in all cases substitute

for

,
has been debunked by the rather simple counterexample

.

We can not allow that utterly ridiculous "axiom" to be shoved down our children's throats!

Don

Sorry Don, but even though

(where

),

Your whole argument is redundant.


Let me explain.

(Notice that it IS possible for

, and that's why I added that important detail in).

Since we have

as well as

, then your logarithmic function (if we choose not to simplify it to

) just illustrates a case where the condition

holds.

The 3D graph of your log function is different than the 3D graph of

, but that has nothing to do with the validity of your argument (it is neither for you nor against you) because the conditions for the values of

and

are not different (you just left out the fact that a can also not be equal to b in your first equation without the logs).

Here's a polynomial function which shows where the condition

must hold:

This supports the other possibility that a can be equal to b (a must be equal to b, that is...just as in your log function where a must not be equal to b....and we are assuming that we don't simplify our functions completely to (b/b)a^3).

An even more trivial case (which you probably thought of but didn't post) for when a must not equal b is:

and so suppose we have:

Again, the graph of

and

are different, but they do not disagree with the conditions.  How could they?  They are equal expressions once you simplify the more complicated one into the simpler one.

Last edited by cmowla (2012-08-05 10:40:08)

That is not an identity when a=b.