# Thread: (x^2)_x = { (100 iff x ≤ 7 ), (x^2 iff x≥ 8) } ?

1. ## (x^2)_x = { (100 iff x ≤ 7 ), (x^2 iff x≥ 8) } ?

Playing around with numbers and I realized this..

(x^2)_x = { (10^2 iff x ≤ 7 ), (x^2 iff x≥ 8) }

Why is this? ( y_x means y converted into base x )

It also works changing the exponent to 3, or 4, or 5, etc.

(x^3)_x = { (10^3 iff x ≤ 7 ), (x^3 iff x≥ 8) }

What is special about the numbers below 8??

Rule: (x^n)_x = { (10^n iff x ≤ 7 ), (x^n iff x≥ 8) }

2. ## Re: (x^2)_x = { (100 iff x ≤ 7 ), (x^2 iff x≥ 8) } ?

Originally Posted by orange gold
Playing around with numbers and I realized this..

(x^2)_x = { (10^2 iff x ≤ 7 ), (x^2 iff x≥ 8) }

Why is this? ( y_x means y converted into base x )

It also works changing the exponent to 3, or 4, or 5, etc.

(x^3)_x = { (10^3 iff x ≤ 7 ), (x^3 iff x≥ 8) }

What is special about the numbers below 8??

Rule: (x^n)_x = { (10^n iff x ≤ 7 ), (x^n iff x≥ 8) }
There is a very strong suspicion in my mind that this is gobbldy-gook (and for that matter that you are a troll)!

What base are the numbers on the right hand side expressed in?

$\displaystyle (x^2)_x=100_x$

for all $\displaystyle x$ not just integer bases (which I will assume $\displaystyle >0$ as I do not want to get into the complication of negative bases)

CB

3. ## Re: (x^2)_x = { (100 iff x ≤ 7 ), (x^2 iff x≥ 8) } ?

I don't think it's true. I think (x^2)_x is always 100_x. For example, (15^2)_15 = 100_15 according to my calculator. Unless I'm not properly understanding what you're doing.

4. ## Re: (x^2)_x = { (100 iff x ≤ 7 ), (x^2 iff x≥ 8) } ?

I don't see why I recieved 5 infractions for this post...
Power hungry??

Anyways, What I am confused about may have something to do with the Wolfram|Alpha calculator then..

when I enter (7^2)_7 it returns 100_7 ==> 49
but when I enter (8^2)_8 it returns 64_8 ==> 52

I don't get why everything before 8 is 100_x ==> x^2 and everything after 8 is (x^2)_x ==> rndm#

5. ## Re: (x^2)_x = { (100 iff x ≤ 7 ), (x^2 iff x≥ 8) } ?

Originally Posted by orange gold
I don't see why I recieved 5 infractions for this post...
Power hungry??

Anyways, What I am confused about may have something to do with the Wolfram|Alpha calculator then..

when I enter (7^2)_7 it returns 100_7 ==> 49
but when I enter (8^2)_8 it returns 64_8 ==> 52

I don't get why everything before 8 is 100_x ==> x^2 and everything after 8 is (x^2)_x ==> rndm#
$\displaystyle (8^2)\text{ base }8$ returns $\displaystyle 100_8$ in Alpha.

(and you did not receive five infractions for your post, you received one infraction worth 5 points, the minimum that you could have received)

CB