I don't think the 18/0 has to do with induction cooking as the AllClad Stainless is magnetic for induction ranges & it has 18/10 interior and exterior. Seems like I've read that the number has to do with how much other alloy is in the stainless steel.

The numbers 18/10 (or 18/8 or 18/0) deal with the percentages of Chromium and Nickel in a stainless steel. The first number is the percentage of Chromium and the second is the percentage of Nickel, so an 18/8 stainless steel contain 18% Chromium and 8% Nickel.

The magnetic properties of stainless steel is determined by it's crystalinne properties. There are two crystaline forms of interest to cooks-austenitic and martensitic.

Pots and pans are generally made of austenitic stainless. It is the most common form of stainless, and is most commonly seen as 18/10 or 18/8, though 18/0 is also available. During manufacturing, it is cooled slowly. It is more corrosion-resistanic because of the large amounts of Chromium and Nickel.

Stainless knives are usually Martensitic stainless. It is cooled rapidly which changes it's crytalline structure, and is thus (usually) magnetic. It contains less Chromium than austenitic steels, and much less Nickel. Howver, it is machainable (austenitic is generally not) and magnetic.

Thus, in a kitchen, we (usually) have pans made of austenitic and knives of martensitic stainless. This is why most stainless pots will not hold a kitchen magnet, but knives can be stored on a magnetic strip.

Here is a link that might be useful: info on stainless steel