Quick question

[lynt.br]

Could someone please explain why

Thanks in advance.

[shinny]

I'm sure others could show it using a much prettier proof, but that's basically showing it through the index law of multiplying powers when you've got a power to another power.

[Flaming_Arrow]

[/0]

For

[TrueTears]

For

Serious? I thought you could have

[lynt.br]

Cheers guys, makes sense now.

[kamil9876]

notice that for natural numbers:

(there are numbers as seen from the subscript). (ask for proof of this if not convinced, I will leave that as a seperate matter)

If

Then the first equation gives:

( terms)





rooting both sides:





Fractional exponents are the much easier way, and in fact you should use them and forget about ath root notation, since the notation of fractional exponents has so much theory loaded into it that it suggests all these non-trivial properties as trivial. However the above argument provides the logical foundations for using fractional exponents and gives motivation for developing theory of them.

[/0]

For

Serious? I thought you could have

While true for certain values of , . In general you can't conclude that

for

e.g.

[TrueTears]

For

Serious? I thought you could have

While true for certain values of , . In general you can't conclude that

for

e.g.

But if true for certain values then you can not say for all

EDIT: "say"

[/0]

For

Serious? I thought you could have

While true for certain values of , . In general you can't conclude that

for

e.g.

But if true for certain values then you can not for all

What do you mean?

[TrueTears]

For

But if for certain values of x satisfies the expression, then you can't say x must be

[/0]

I didn't say that you must have . It is simply a subset of the values can take.
However, if you want to make negative then you must simultaneously introduce restrictions on and which can make things very tricky.

You cannot simply say

for all x if you get my drift.

[TrueTears]

For

implies you mean for all

or why would you even mention a subset of the domain?

It's like saying you got with no restriction yet I'm gonna put after it since it's a subset.

Soz I'm just not getting the point if you know what I mean.

[/0]

For

implies you mean for all

Gee, I think you're right about that.

It is defined for all right, so there's nothing wrong about that?
 
It is all we will need to worry in VCE, and if you want to write up the restrictions for and , be my guest.

[TrueTears]

Yes it is defined but I don't see the point of writing it, like I said is defined for right? But why would you even put a subset after the expression.