You first step concludes that if then .
Your second step concludes that if then
The second step says that g(x) satisfies the condition in the first step so you replace "x" in the first step by "g(x)".
there is , is continues in
point. i need to prove that
by epsilon delta definition.
i need to follow only my books prove.help me understand it.
the books proof:
in order to prove
we will use the definition that for
surrounding we have surrounding for which every
is continues in point. so
and for surrounding we have
surrounding for which every
it is given that then for
cant understand this last step why
is the resolt of the last two steps??
but we have different deltas in each limit
the first is delta1 the other is just delta.
and g doesnt satisfies the first one
because its a different surroundings
cant see wht we replace x with g(x)
why g(x) suttisfies the first step?
ok i start to understand the idea
how do i know that if we put g(x) instead of x
i get an input of 'x' in f(x) for which this 'x' is inside the section bounded by delta1
maybe this 'x' is out side the section bounded by delta1.
we dont know what is g(x) we can put some x which is bounded by the minimal delta
and get alot bigger number
and get fg(a)=f(1000)
and this 1000 could be higher the the minimal delta