Understanding the 4-Ball: ||x|| ≤ r

[stanford1463]

Homework Statement

What is the x-simple description of a 4-ball = { ||x|| \leq r }

Homework Equations

It's a 4-ball, so isn't the equation x^{2} + y^2 +z^2 +w^2 ?

The Attempt at a Solution

For my limits, I got x is between \pm \sqrt{1-z^2} and y is between -1 and 1, and z is between \pm \sqrt{1-x^2-y^2}, and w is between \pm \sqrt{1-x^2-y^2-z^2} Is this right? Thanks!

 

[stanford1463]

buuumppp...please help! Any advice is good!

 

[Mark44]

Homework Statement

What is the x-simple description of a 4-ball = { ||x|| \leq r }

Homework Equations

It's a 4-ball, so isn't the equation x^{2} + y^2 +z^2 +w^2 ?

That couldn't possibly be the equation. An equation always states that two expressions have the same value. I see only one expression, and even more to the point, I don't see an equals sign.

What does x-simple description mean?

The Attempt at a Solution

For my limits, I got x is between \pm \sqrt{1-z^2} and y is between -1 and 1, and z is between \pm \sqrt{1-x^2-y^2}, and w is between \pm \sqrt{1-x^2-y^2-z^2} Is this right? Thanks!

Where did the 1 come from?