Can you please explain "to within"?


Maybe this example will help.

Pour the hot brine into the jars, filling them to within a half-inch of the top.

This means that the final level of the water should be a little less than a half-inch from the top. It could be 1/8 inch from the top, 1/4 inch from the top, or 3/8 inch from the top, and so on — anywhere from 1/2 inch from the top to exactly at the top.

I can't answer specifically for your mathematical example, but it must be something like this. Some mathematical entity has a lower bound that is "somewhere near" this constant factor that they mention in the text.



Thanks a lot CJ Emotion: smile