Question

I'm studying limits on Pauls Online Notes, and the 2nd property of limits he mentions is:
lim [f(x)+g(x)] = lim f(x) + lim g(x)

But what if
f(x) is a step function where y=0 if x < 0 and y=1 if x >= 0
g(x) is a step function where y=1 if x < 0 and y=0 if x >= 0

f(x) + g(x) will have y=1 for all values, hence I believe the limit at 0 would be 1.

But the limit of f(x) does not exist. So how is the property true?

Is this property true only if lim f(x) and lim g(x) exist?

Answer 1

I went to the proof section of the site and it said "assume f(x) and g(x) exist", so I guess that answers my question.