Don:
I am beginning to see that you have a valid point there. I must admit that the math over there is beyond my skills, but I can see how, when doing a certain type of algebraic menipulation on a function that involves natural logarithms, and a function of the type
something special (and beyond my understanding) happens.
BUT…what about the more obvious things?
And I will give a few examples
1.
if not the same as
because T might be equal to zero, in which case
is indeterminate !
2. When working with exponents
is not always legal, since if a is a negative number the exponent cannot be a fraction since
has no real answer.
3.
is not the same as x, since if x is negative, it will become a positive !
this list can go on forever, i just came up with a couple examples from my fairly basic knowledge in math, but I believe that this kind of concepts are absolutely essential if you want to
understand basic mathematics.
How many students are aware of the fundamentals? How many year 12 students who have taken calculus are capable doing simple differentiation using first principals?
How many students know where e, the natural logarithm comes from or are capable of writing and explaining for formula for the series that generates e?
(its
by the way. just punch into a grahpics calculator
:
(1+(1/(2^96)))^(2^96) = 2.7182818284590452353602874713355
e^1 = 2.7182818284590452353602874713527
(This was fun
)
I would even challenge the teachers here to see what percentage of their students know that 'ln' is simple
(!)
If I where to use the word emergency, I would use it for this kind of thing. this is not something that concerns mathematicians, but also scientists and engineers (those are the epoeple that have made it possible for this forum to exist through microchips and magnetic drives and stuff like that). They use this level of math all the time and yet a large portion of them are clueless when it comes to actually understanding this level of mathematics.
