- #1
Miike012
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Theorem: If f approaches l and g approaches m neer a then
lim(f+g) = l + m as x approaches a
Proof:
If 0 < | x - a | < delta1, then |f(x) - l| < epsilon,
and If 0 < | x - a | < delta2 then |g(x) - m| < epsilon,
If 0 < | x - a | < delta1, then |f(x) - l| < epsilon / 2,
and If 0 < | x - a | < delta2 then |g(x) - m| < epsilon/2,
Now Let Delta = min(delta1,delta2). If 0 < | x - a | < delta, then 0 < | x - a | < delta1 and
0 < | x - a | < delta2 are both true, so both
|f(x) - l| < epsilon / 2 and |g(x) - m| < epsilon/2 are true and |(f + g)(x) - (l + m)| < epsilon.
I understand what the theorem is saying but when it goes into proving the theorem I don't fully understand the logic. I have never had any formal class on proofs and I am trying to read through this book but it takes me 2-3 hours to get through one chapter then at the end I still don't fully understand the material. My question is, will taking a discrete mathematics class, if I am right this is kind of like a intro to math proofs and logic, should it make understanding proofs like this and harder ones easier to understand? If not this class, are there any other classes that I can take?
I'm thinking if I don't understand something as "easy" as this proof then I am not ment for math, even though I average 95-97 on math tests, but that obviously meens nothing.
lim(f+g) = l + m as x approaches a
Proof:
If 0 < | x - a | < delta1, then |f(x) - l| < epsilon,
and If 0 < | x - a | < delta2 then |g(x) - m| < epsilon,
If 0 < | x - a | < delta1, then |f(x) - l| < epsilon / 2,
and If 0 < | x - a | < delta2 then |g(x) - m| < epsilon/2,
Now Let Delta = min(delta1,delta2). If 0 < | x - a | < delta, then 0 < | x - a | < delta1 and
0 < | x - a | < delta2 are both true, so both
|f(x) - l| < epsilon / 2 and |g(x) - m| < epsilon/2 are true and |(f + g)(x) - (l + m)| < epsilon.
I understand what the theorem is saying but when it goes into proving the theorem I don't fully understand the logic. I have never had any formal class on proofs and I am trying to read through this book but it takes me 2-3 hours to get through one chapter then at the end I still don't fully understand the material. My question is, will taking a discrete mathematics class, if I am right this is kind of like a intro to math proofs and logic, should it make understanding proofs like this and harder ones easier to understand? If not this class, are there any other classes that I can take?
I'm thinking if I don't understand something as "easy" as this proof then I am not ment for math, even though I average 95-97 on math tests, but that obviously meens nothing.