2: 15 I do not understand how the example is tied to the definition. Why do we take x outside Z ? Based on the definition, shouldn't we take x from the closure of Z which is Z again??
Hello, I think you’re confusing the notation. Here the “bar” denotes closure, not complement. So I am saying x is in the closure of Z, which is Z, like you said.
So far the most intuitive explanation of the concept of nowhere dense sets that I saw on the internet. Thank you for making this video!
Thank you, that’s nice to hear. I’m glad it was helpful!
Incredible explanation. Thanks so much!!!
Glad it was helpful!
I see. You’re right that I’m not using the definition in 2:05. Instead I’m showing an equivalent statement that R/Z is a dense open subset of R.
In 8:40 you say we're allowed to take that radius r_1 such that 0
Yes that sounds right, we use that property to get the nice pattern for the different radii.
2: 15 I do not understand how the example is tied to the definition. Why do we take x outside Z ? Based on the definition, shouldn't we take x from the closure of Z which is Z again??
Hello, I think you’re confusing the notation. Here the “bar” denotes closure, not complement. So I am saying x is in the closure of Z, which is Z, like you said.
Your example just doesn't make any sense.@@DrMcCrady
@@zwan1886can you be more specific?
The conditions given in 2:05, I don't see how they are related to the example given at 2:45@@DrMcCrady
nice video!
Thank you!