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#### LeibnizIsBetter

##### MHB Donor

- Aug 28, 2013

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I know this is probably the most basic question imaginable so please bear with me. I did google it but I still couldn't figure it out.

Say you have a function \(\displaystyle f(x, y, z)\) and a point \(\displaystyle (x_0, y_0, z_0)\) that satisfies the equation \(\displaystyle f(x, y, z) = 0\).

Does that imply that \(\displaystyle f(x_0, y_0, z_0) \in f(x, y, z)\) ? Where \(\displaystyle \in\) means "is an element of".

Or, what's the relationship between \(\displaystyle (x_0, y_0, z_0)\) and \(\displaystyle f(x, y, z)\) if \(\displaystyle (x_0, y_0, z_0)\) is a point on the surface defined by \(\displaystyle f(x, y, z) = 0\)?

Thanks so much. I'm new to this and didn't drink enough coffee today.

Say you have a function \(\displaystyle f(x, y, z)\) and a point \(\displaystyle (x_0, y_0, z_0)\) that satisfies the equation \(\displaystyle f(x, y, z) = 0\).

Does that imply that \(\displaystyle f(x_0, y_0, z_0) \in f(x, y, z)\) ? Where \(\displaystyle \in\) means "is an element of".

Or, what's the relationship between \(\displaystyle (x_0, y_0, z_0)\) and \(\displaystyle f(x, y, z)\) if \(\displaystyle (x_0, y_0, z_0)\) is a point on the surface defined by \(\displaystyle f(x, y, z) = 0\)?

Thanks so much. I'm new to this and didn't drink enough coffee today.

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