Is a function [math] f [/math] uniformly continuous at any interval that is a single point? So if the interval is [1,1], would the function be uniformly continuous? Or would it actually depend on what the function is?
>>8011817
what is your definition of uniformly continuous? if you're using the same one as wikipedia at least, then uniform continuity is a global condition and it doesn't even make sense to check it at a point.
>>8011817
Are you high? Look at the definition again,look at your post,contemplate suicide,do it.
A point is an interval though
Still trying to figure out why you posted a fractal with this
>>8011880
Bc it looks cool
>>8011817
Yes, but it is an exceptionally useless property since it completely misses the point of continuity and especially uniform continuity
Could you say that if an interval is defined as a single point [1,1], it could not be uniformly continuous since the distance between a point and itself is 0?
>>8011940
I could see how it's useless but it still is technically not uniformly continuous.
>>8011866
Continuity doesn't make sense for zero-length intervals (i.e. isolated points). If it did, then it would stop making sense altogether.
>>8012005
So if an interval is defined as a point, it can not be uniformly continuous.
>>8011977
Sure it is, a function on a one-point line segment is automatically continuous and, hence, uniformly continuous (as a singleton is compact)
>>8012090
as long as the point isn't a point of discontinuity
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>>8012754
how desu?
