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# A question about limits Tweet

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Why does [x+y]<= [x] + [y]

equal

[x]-[y]<=[x+y]

where [x] is the modulus/absolute value of x
2. Re: A question about limits
Rewrite x+y as a, and y as -b, and see what comes out.
3. Re: A question about limits
(Original post by anonstudent1)
Why does [x+y]<= [x] + [y]

equal

[x]-[y]<=[x+y]

where [x] is the modulus/absolute value of x
I will show that and are equivalent. First, set in to obtain . Then, set in to obtain .
4. Re: A question about limits
(Original post by Hopple)
Rewrite x+y as a, and y as -b, and see what comes out.
[a]<=[x]-[b]

[x]+[b]<=[a]
5. Re: A question about limits
(Original post by anonstudent1)
[a]<=[x]-[b]

[x]+[b]<=[a]
x = a+b, and |-b| = |b| Also, how did you get from the first line of that to the second?
6. Re: A question about limits
(Original post by Hopple)
x = a+b, and |-b| = |b| Also, how did you get from the first line of that to the second?
Ok i get i understand now. Thanks for your help!
7. Re: A question about limits
(Original post by Hopple)
x = a+b, and |-b| = |b| Also, how did you get from the first line of that to the second?
Wait sorry i don't understand lol

Ok so i get

[a]<= [a+b] - [b]

How do i go from there to get

[a+2b] <= [x]+[y]

?
8. Re: A question about limits
(Original post by anonstudent1)
Wait sorry i don't understand lol

Ok so i get

[a]<= [a+b] - [b]

How do i go from there to get

[a+2b] <= [x]+[y]

?
nohomo's basically written it all out, but doing as I said, you'll get the first inequality becoming |a| <= |a+b| + |b|
9. Re: A question about limits
(Original post by nohomo)
I will show that and are equivalent. First, set in to obtain . Then, set in to obtain .
Thank you!