Tom,
The term "infinite" is used to describe anything so numerous as to be impossible to count. Look up in the sky and see an infinite number of stars. Now let's see how we can apply infinite to electricity.
To start with, "ohm's" are a measurement term for resistance. When you apply voltage to a circuit, you allow "current" to flow. For example, hook up a light bulb to a 12 volt battery. The filiment that glows is actually a resistor so to speak. The resistance to the flow of current generates heat and hence light. Higher current flow means more heat, more light. Less current flow, less heat less light. Did you ever notice some lights seem to become brighter just prior to blowing? The filiment is burning up, less resistance, more light. The filiment blows, no light, no measureable resistance.
Further, lets say you have two light bulb's. One 60 watt, one 100 watt. If you were to measure the resistance, the 60 watt bulb would actually measure higher in value. Now, you drop that bulb and the filiment breaks. You have no physical connection so you cannot measure resistance at all. It's there though.
Now, lets take your coil and put the ohmmeter probes on it. Let's say your meter has an analog guage (not digital) and the needle pegs to the right. This could mean a couple of things. One, you have a broken wire within the coil. No current flow is possible. You cannot measure the value of resistance. Two and less likely, your meter just does not measure that high.
Been a long time since I had my face in a basic electricity book but I hope this helps.