school ranks? + absolute vaules (2 Viewers)

[super.muppy]

can someone post up the school ranks

and

prove |a+b| smaller or equal to |a|+|b| for all real a,b

Ty

 

[georgia-ellen]

Hey, I could be wrong I haven't completely grasped absolute values yet
but I'm pretty sure |a+b| doesnt equal |a|+|b|
like for example, if a = 2, b= -4
|a+b|
|2-4|
= 2
whereas
|2|+|-4|
= 6

perhaps there's a rule I don't understand yet?
Sorry if I've confused you further

 

[georgia-ellen]

Ohh sorry! I just read that it was smaller than or equal to
Yeah that's correct
I forget how I'm meant to prove it though hahaha
when I revise I'll reply

 

[P.T.F.E]

|a+b|=a+b or -a-b
where as |a|+|b|=a+b
therefore because -a-b is a negative it must be less than a+b
therefor |a+b|=|a|+|b|or |a+b|<|a|+|b|

 

[super.muppy]

ty everyone

 

[khorne]

You should be aware that -|a| <= a <= |a| and that |a| <= k (only if -k <= a <= k)

Therefore from |a+b| <= |a|+|b|, we reason (from the first property) that it is equal to -(|a|+|b|) <= a+b <= |a|+|b|

And if we assume k = |a| + |b|, we conclude by saying

|a+b| <= |a|+|b| (using property 2)

I hope this made sense, just tell me if you want a further explanation

 

[super.muppy]

ur in yr 10?

 

[khorne]

Indeed I am

 

[tommykins]

Hey, I could be wrong I haven't completely grasped absolute values yet
but I'm pretty sure |a+b| doesnt equal |a|+|b|
like for example, if a = 2, b= -4
|a+b|
|2-4|
= 2
whereas
|2|+|-4|
= 6

perhaps there's a rule I don't understand yet?
Sorry if I've confused you further

a = 1, b = 1

|1+1| = 2
|1|+|1| = 2

.'. true.

|a+b|=a+b or -a-b
where as |a|+|b|=a+b
therefore because -a-b is a negative it must be less than a+b
therefor |a+b|=|a|+|b|or |a+b|<|a|+|b|

doesn't make sense.

You should be aware that -|a| <= a <= |a| and that |a| <= k (only if -k <= a <= k)

Therefore from |a+b| <= |a|+|b|, we reason (from the first property) that it is equal to -(|a|+|b|) <= a+b <= |a|+|b|

And if we assume k = |a| + |b|, we conclude by saying

|a+b| <= |a|+|b| (using property 2)

I hope this made sense, just tell me if you want a further explanation

lol, closest one to the answer, but still not entirely correct.

this is however a 4unit question.

 

[agirlinatutu]

Indeed I am

we found a year 10'er that knows what hes talking about.

 

[khorne]

this is however a 4unit question.

Is it? I thought it was part of the 3 unit syllabus, which would make sense if they asked you a question about it in the Fitzpatrick (I assume) book?

 

[tommykins]

Is it? I thought it was part of the 3 unit syllabus, which would make sense if they asked you a question about it in the Fitzpatrick (I assume) book?

it has to deal with complex number vectors, where |z1|+|z2| >=|z1+z2|

it is called the triangle inequality where two sides of a triangle ALWAYS add up to be greater or equal the third side.

equality holds when it is a straight line.

 

[super.muppy]

im doing revision booklets we got tests comming up already :angry:

 

[khorne]

Yeah, so do we =D

I was wondering, if it's the same for your school, as they are giving us a set of problems, eg (100) and from those 100 they will select the final questions for the test. So theoretically you can score 100% before the test if you can do all the questions

 

[super.muppy]

nope

 

[xXmuffin0manXx]

but if you're proving using examples
you cant just give 'a' and 'b' any real value

you would have to say 'let a= etc etc'