Science Forums 2

[Don Blazys]

To:CraigD. If we begin with the term:

(T/T)a^x,

then "crossing out" the cancelled T's leaves us with:

a^x,

and if all we are left with is:

a^x,

then we can't possibly derive the more defined and powerfull term:

T(a/T)^((xln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1)).

That's one reason why I am against teaching students that they should automatically "cross out" cancelled common factors. I believe that students should be taught the truth, and the truth is that when confronted by a term such as:

(T/T)a^x,

they have a choice. They can either "lose" or "cross out" the cancelled T's and write:

a^x,

or, they can choose to retain the cancelled T's and write:

T(a/T)^((xln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1)),

where it is now algebraically impossible to "lose" or "cross out" the cancelled T's. Before I invented the above "cohesive term", we didn't have this choice!

Now, the question is, if a "common factor" is defined as a positive integer T>1, then which term should we use for problems that involve cancelled "common factors"...

a^x

or

T(a/T)^((xln(a)/(ln(T))-1)/(ln(a)/(ln(T))-1)) ?

I prefer the "cohesive term". How about you?

Don.