The Ultimate One

[%BlueSoulRobot%]

Hey, how is it that when I punch in a random whole number (for example 755) on the calculator, and keep pressing the square root function, the ultimate answer is One? I mean, 1 multiplied by itself is one, so how can the last answer be one?*

*Discovered while bored in math class,

The same thing goes for a decimal: any decimal will eventually turn into 0.9999998 using the repeated squareroot function pressing method.

:bugeye:
- %Blue%

 

[BobG]

I think its probably the calculator rounding down to one when it runs out of place

 

[%BlueSoulRobot%]

Really?

 

[Crisp]

Hi,

A not too mathematical explanation:

Denote x any random number
-> sqrt(x) = x^(1/2)
-> sqrt(sqrt(x)) = x^(1/4)

after n runs:

-> sqrt(...sqrt(sqrt(x))...) = x^(1/2^n)

The limit n -> infinity of (1/2^n) = 0, and hence in the end you get:

lim_(n->inf) x^(1/2^n) = x^0 = 1

You get this in a finite amount of sqrt's because of the rounding errors in your calculator.

Bye!

Crisp

 

[%BlueSoulRobot%]

I see! Thanks Crisp!

And I thought I had discovered something amazing and revolutionary, when it turned out to be my calculator's fault. Dang.