Apologize for troll, but I have one question...

Question

anonymous · Answer

Once I plot y = x^y, I notice that it does not pass vertical line, hence not function. i dont understand one thing... it can be rewrite as y = x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x^x... 

why is it not function?

anonymous · Answer

y = x is function, y = x^x is function, y = x^x^x is function too and so on. why isnt y=x^y function?

anonymous · Answer

i think because to re-write that, you plug the function into itself, which doesnt work

lgbasallote · Answer

whoever said y = x^y isn't a function?

anonymous · Answer

Well, it doesnt follow the pattern (see my second reply) if the number of exponent is finite, it is function, otherwise its not. why?

anonymous · Answer

@lgbasallote plot it yourself and you can notice it doesnt pass vertical line test

lgbasallote · Answer

if you try to solve for x

y = ylnx
y/y = lnx

1 = lnx

can you now see why it's not a function?

anonymous · Answer

should have thought of that. thanks

hartnn · Answer

what the ... ?

lgbasallote · Answer

but seriously...who said it isn't a function?

hartnn · Answer

ln y = ylnx

lgbasallote · Answer

and...what did i just do?

anonymous · Answer

@lgbasallote  well, it isnt, right?

anonymous · Answer

you just proved this.

lgbasallote · Answer

@hartnn exactly..that's why i'm wondering why qwerties is saying it isn't a function

anonymous · Answer

wait...

lgbasallote · Answer

@qwerties i manipulated my algebra to make it look like not a function

lgbasallote · Answer

but if you look carefully there is a fallacy in my solution

anonymous · Answer

well, it doesnt pass vertical test.

 can you explain it?

anonymous · Answer

if it doesnt pass vertical line test, is it mean it still can be function?

lgbasallote · Answer

y = x^y according to my math vocabulary is what others call a recursive "function"