Without knowing anything about the values, how can this be true?

>>8461412
are you retarded?

this is stating that no matter what, if the absolute value of a-b is less than c, then b-c is less than a. bidirectional.

>>8461419
It only works if a is lesser than b. Otherwise that's what I don't understand.

>>8461412
la - bl < c iff
a - b < c AND b - a < c

>>8461429
That's what I thought, you cannot take one case into consideration without forgetting the second, right? For in my maths notes only one is taken for all the rest of the deductions, it might be wrong.

c is positive.
a lies in an open interval with radius c and centre b
b-c is the infimum of this set. therefore a>=b-c
but a cannot equal b-c because the interval is open

>>8461442
if c was positive then shouldn't it say | a - b | < |c| <=> b - |c| < a ?

>>8461412
to get the left arrow it's just
| a - b | < c
- c < a - b < c
- c < a - b /\ a - b < c
- c < a - b
b - c < a

for the right it's
b - c < a
- c < a - b
the rest is trivial and left as an exercise to the reader
| a - b | < c

therefore, | a - b < c <-> b - c < a

>>8461453
Now I understand, thank you.

>>8461412
its wrong, take a=1, b=0 and c=-0.5

>>8461453
>the rest is trivial and left as an exercise to the reader
LELELELELELELELELEL

take a=3
b=0
c=2
the double implication is bollocks