anonymous
  • anonymous
Is any taking a transition to advanced mathematics course? I need help with a proof!!!
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
what kind of proof?
anonymous
  • anonymous
I need to prove that \[|a+b| \le|a|+|b|\] and I know that it has to do with proof by cases
anonymous
  • anonymous
ok, can see why this relationship holds before even starting?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
no..not really :( that is why I want to understand why this is the case and how I go about proving this to be true
anonymous
  • anonymous
ok, so we have the absolute value of the sum of A and B. then the sum of the absolute value of A with the absolute value of B
anonymous
  • anonymous
oh and we are assuming that a and b are real numbers
anonymous
  • anonymous
sure, so any number, positive or negative, when put in the absolute value function yields a postive
anonymous
  • anonymous
roughly speaking
anonymous
  • anonymous
yes
anonymous
  • anonymous
so, assume A and B are of opposite sign. if we take the absolute value of A, then abs of B, both will come out as positive numbers...this is basically the right hand side...so the right hand side is always positive, right?
anonymous
  • anonymous
yes so that would be Case 1. right then we would have another case were both A and B are positive and A and B are both negative?
anonymous
  • anonymous
let's still look at case 1 as you say with A and B of opposite sign....so if we sum A and B, the sum could be positive or negative, depending upon the magnitude of each....
anonymous
  • anonymous
A+B < 0, or > 0, or = 0 (if A=(-B))
anonymous
  • anonymous
doesn't the absolute value make the sum of A and B postive ?
anonymous
  • anonymous
but in anycase, if of opposite sign, their sum will be less than the sum of two positive values
anonymous
  • anonymous
we are looking at left hand side now, we know right will always be positive...but we are looking inside the absolute value function, looking right at the sum of A and B before we put that sum through the absolute value function
anonymous
  • anonymous
haha, sorry if I confused you, does it make sense so far?
anonymous
  • anonymous
hi sorry I couldn't post
anonymous
  • anonymous
yeah, you can refresh the page when it gets stuck
anonymous
  • anonymous
so I am confused as to why the right side would always be positive? can you explain that again?
anonymous
  • anonymous
ok, how does the absolute value function work? what is the result of abs(5), what is the result of abs(-5)?
anonymous
  • anonymous
it would be 5 in both cases. The absolute value always produces a positive answer
anonymous
  • anonymous
right on, ok, the right side of the equation is \[\left| a \right| + \left| b \right|\]
anonymous
  • anonymous
"The absolute value always produces a positive answer"
anonymous
  • anonymous
"The absolute value always produces a positive answer"
anonymous
  • anonymous
abs(a) is going to be positive, abs(b) is going to be positive as you pointed out
anonymous
  • anonymous
the sum of two positive values is positive
anonymous
  • anonymous
right. I think i see why the right side would always be bigger than the left, because on the right we are adding two variables after we take the absolute value of each individually whereas on the left we add them together first and then take the absolute value. Right?
anonymous
  • anonymous
yes man...so back to the idea that A and B are of opposite sign
anonymous
  • anonymous
yes man...so back to the idea that A and B are of opposite sign
anonymous
  • anonymous
we know the right side will be positive, and well we know the left side will be positive because everything happens in the absolute value function
anonymous
  • anonymous
This proof is confusing because we have to consider both A and B with positive and negative values
anonymous
  • anonymous
right, that's the tricky part, and that's what the equation is telling you
anonymous
  • anonymous
brb
anonymous
  • anonymous
ok
anonymous
  • anonymous
okay
anonymous
  • anonymous
so can you answer it?
anonymous
  • anonymous
case 1 = opposite sign, case 2 = same sign
anonymous
  • anonymous
sorry again it didn't let me post
anonymous
  • anonymous
would we have to consider greater than or equal to zero when we are doing the case where both are positive?
anonymous
  • anonymous
and the same for the opposite sign one?
anonymous
  • anonymous
you still there?
anonymous
  • anonymous
when both are positive, you can ignore absolute vlaue functions right?
anonymous
  • anonymous
it's as though that work has already been done...
anonymous
  • anonymous
yes...but we cant when we are dealing with opposite signs
anonymous
  • anonymous
right, when the signs are the same, it's not difficult, when signs are opposite, the sum of the values can either be positive or negative (so before applying right hand side absolute value on A + B, that sum could be greater than 0, less than 0 or 0.
anonymous
  • anonymous
so I am confused whether that would be a single case or 3?
anonymous
  • anonymous
so, ok, keep it as single case with 3 parts, haha..you're right, do it as 3
anonymous
  • anonymous
couldn't we do the case for when they are both positive and both negative and then just use Without Loss of Generality? since their proofs are going to be identical?
anonymous
  • anonymous
i guess, imagine a number-line, the both positive case takes place to the right of 0, while the both negative case takes place to the left of 0...but then the absolute value functions flip the result to be similar to that of the case of both positive
anonymous
  • anonymous
draw the function abs(x) on a graph right now and look at the result for y...y=x, of y=f(x), where f(x) = abs(x)..i've got to go, but i can get on later
anonymous
  • anonymous
okay thanks for your help though. I appreciate it

Looking for something else?

Not the answer you are looking for? Search for more explanations.