Conquer Club

Ok, here's what I was thinking in calc the other day, if 2+2+2=2*3 and 2*2*2=2^3, what does 2^2^2=?, is there some higher function for this? From there, is there some sort of infinite higherarchy? And is this even a useful function?

maasman wrote:Ok, here's what I was thinking in calc the other day, if 2+2+2=2*3 and 2*2*2=2^3, what does 2^2^2=?, is there some higher function for this? From there, is there some sort of infinite higherarchy? And is this even a useful function?

And your enjoyment of The Big Bang Theory now becomes clear. <smile>

I like math quite a lot, and since I just took the BC calc test, we don't have anymore homework and class is pretty light and laid back, which gives me a lot of time to think

Yes, it's called the Army of GOD function.

2(hurrdurr)3=2^2^2

Army of GOD wrote:Yes, it's called the Army of GOD function.

2(hurrdurr)3=2^2^2

Not quite what I was looking for, but I'll take it for now

The real question is whether .999... = 1

Neoteny wrote:The real question is whether .999... = 1

I believe that already has its own thread and broke down into name calling and feces throwing.

AgentSmith88 wrote:

Neoteny wrote:The real question is whether .999... = 1

I believe that already has its own thread and broke down into name calling and feces throwing.

Well at least I'm not a facehead.

*puts cupped hand near ass*

Is there a "Legends of the Hidden Temple" thread? If not you should start one AoG.

If Nickelodeon can give me the rights, I'd remake the whole friggin' show.

maasman wrote:Ok, here's what I was thinking in calc the other day, if 2+2+2=2*3 and 2*2*2=2^3, what does 2^2^2=?, is there some higher function for this? From there, is there some sort of infinite higherarchy? And is this even a useful function?

No. Addition and Multiplication are associative functions, which means the order you do them in doesn't matter (ie x+y+z= z+x+y= y+x+z etc) but "Raising to the power of..." (for want of a snappier title) is not associative and must be explicitly ordered with brackets for accuracy, so x^(y^z) is not always equal to (x^y)^z except in a very few certain cases. Thus there is no infinite hierarchy.

maasman wrote:Ok, here's what I was thinking in calc the other day, if 2+2+2=2*3 and 2*2*2=2^3, what does 2^2^2=?, is there some higher function for this? From there, is there some sort of infinite higherarchy? And is this even a useful function?

I think you mean is there some simplifying term for this? Not off of the top of my head. Note that you can "cheat" to some extent because the log function effectively bumps math down one level 2^3 = e^(ln(2)*3) so the operation 2?3 could also be defined as e^(ln(2)^3) or even (he he) e^(e^(ln(2)*3))

I don't think this is a useful function.

Lord+Master wrote:

maasman wrote:Ok, here's what I was thinking in calc the other day, if 2+2+2=2*3 and 2*2*2=2^3, what does 2^2^2=?, is there some higher function for this? From there, is there some sort of infinite higherarchy? And is this even a useful function?

No. Addition and Multiplication are associative functions, which means the order you do them in doesn't matter (ie x+y+z= z+x+y= y+x+z etc) but "Raising to the power of..." (for want of a snappier title) is not associative and must be explicitly ordered with brackets for accuracy, so x^(y^z) is not always equal to (x^y)^z except in a very few certain cases. Thus there is no infinite hierarchy.

This is true but the idea is that we are dealing with iterative functions, the same number repeated again and again, so the "order" is implied.

Multiplication is repeated addition
Exponenation is repeated multiuplication
Maasmanation is repeated exponenation.

its 2^4 guys...... simplify.

Neoteny wrote:The real question is whether .999... = 1

Actually, I believe we definitively proved it did in another thread.










or didnt...

edocsil wrote:its 2^4 guys...... simplify.

No, it's 4^2

Does 3^3^3^3 = 3^(3*3) or is that something different?

nippersean wrote:Does 3^3^3^3 = 3^(3*3)

No.

or is that something different?

Yes.

x^y^z is not well-defined.

It needs to be specified as either (x^y)^z OR x^(y^z)

MeDeFe wrote:

edocsil wrote:its 2^4 guys...... simplify.

No, it's 4^2

lol

10000 (binary, of course!)

Trephining wrote:x^y^z is not well-defined.

It needs to be specified as either (x^y)^z OR x^(y^z)

While that's true, the rather obvious implication from the first post is that he's looking for terms of the form

(x^x)^x or ((x^x)^x)^x or (((x^x)^x)^x)^x etc.

As long as we're agreed that each exponent is meant only to raise what's below it, then we can safely multiply all the exponents together. I'm not sure if that applies to an infinite number of exponents, though, given the existence of the http://en.wikipedia.org/wiki/Riemann_series_theorem.

MeDeFe wrote:

nippersean wrote:Does 3^3^3^3 = 3^(3*3)

No.

or is that something different?

Yes.

3^3^3^3= 3^(3*3*3)

tzor wrote:

Lord+Master wrote:

maasman wrote:Ok, here's what I was thinking in calc the other day, if 2+2+2=2*3 and 2*2*2=2^3, what does 2^2^2=?, is there some higher function for this? From there, is there some sort of infinite higherarchy? And is this even a useful function?

No. Addition and Multiplication are associative functions, which means the order you do them in doesn't matter (ie x+y+z= z+x+y= y+x+z etc) but "Raising to the power of..." (for want of a snappier title) is not associative and must be explicitly ordered with brackets for accuracy, so x^(y^z) is not always equal to (x^y)^z except in a very few certain cases. Thus there is no infinite hierarchy.

This is true but the idea is that we are dealing with iterative functions, the same number repeated again and again, so the "order" is implied.

Multiplication is repeated addition
Exponenation is repeated multiuplication
Maasmanation is repeated exponenation.

Mathematics is inherently abhorrent of ambiguities so to state that the order is implied is simply not good enough! It's either stated clearly and obviously and unambiguously or... it's not proper maths

Anyway, as 2*2 = 2^2, "maasmanation" (nice term btw!) is no more than what you term "exponenation" (which I'm very dubious is a real term tbh) and, furthermore, in this isolated example, no more than multiplication.

I still say no to the original question...

MeDeFe wrote:

edocsil wrote:its 2^4 guys...... simplify.

No, it's 4^2

No, it's 16^1.

MeDeFe wrote:

nippersean wrote:Does 3^3^3^3 = 3^(3*3)

No.

or is that something different?

Yes.

Thanks for the incite MDF, most helpful.