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anonymous
 5 years ago
Is any taking a transition to advanced mathematics course? I need help with a proof!!!
anonymous
 5 years ago
Is any taking a transition to advanced mathematics course? I need help with a proof!!!

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I need to prove that \[a+b \lea+b\] and I know that it has to do with proof by cases

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, can see why this relationship holds before even starting?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no..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
 5 years ago
Best ResponseYou've already chosen the best response.0ok, 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
 5 years ago
Best ResponseYou've already chosen the best response.0oh and we are assuming that a and b are real numbers

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sure, so any number, positive or negative, when put in the absolute value function yields a postive

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, 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
 5 years ago
Best ResponseYou've already chosen the best response.0yes 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
 5 years ago
Best ResponseYou've already chosen the best response.0let'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
 5 years ago
Best ResponseYou've already chosen the best response.0A+B < 0, or > 0, or = 0 (if A=(B))

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0doesn't the absolute value make the sum of A and B postive ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but in anycase, if of opposite sign, their sum will be less than the sum of two positive values

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we 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
 5 years ago
Best ResponseYou've already chosen the best response.0haha, sorry if I confused you, does it make sense so far?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hi sorry I couldn't post

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, you can refresh the page when it gets stuck

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so I am confused as to why the right side would always be positive? can you explain that again?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, how does the absolute value function work? what is the result of abs(5), what is the result of abs(5)?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it would be 5 in both cases. The absolute value always produces a positive answer

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right on, ok, the right side of the equation is \[\left a \right + \left b \right\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0"The absolute value always produces a positive answer"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0"The absolute value always produces a positive answer"

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0abs(a) is going to be positive, abs(b) is going to be positive as you pointed out

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the sum of two positive values is positive

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right. 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
 5 years ago
Best ResponseYou've already chosen the best response.0yes man...so back to the idea that A and B are of opposite sign

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes man...so back to the idea that A and B are of opposite sign

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0we 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
 5 years ago
Best ResponseYou've already chosen the best response.0This proof is confusing because we have to consider both A and B with positive and negative values

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right, that's the tricky part, and that's what the equation is telling you

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so can you answer it?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0case 1 = opposite sign, case 2 = same sign

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0sorry again it didn't let me post

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0would we have to consider greater than or equal to zero when we are doing the case where both are positive?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and the same for the opposite sign one?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when both are positive, you can ignore absolute vlaue functions right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it's as though that work has already been done...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes...but we cant when we are dealing with opposite signs

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0right, 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
 5 years ago
Best ResponseYou've already chosen the best response.0so I am confused whether that would be a single case or 3?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so, ok, keep it as single case with 3 parts, haha..you're right, do it as 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0couldn'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
 5 years ago
Best ResponseYou've already chosen the best response.0i guess, imagine a numberline, 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
 5 years ago
Best ResponseYou've already chosen the best response.0draw 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
 5 years ago
Best ResponseYou've already chosen the best response.0okay thanks for your help though. I appreciate it
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