Triangle Inequality Proof

We prove that |x+y| is less than or equal to |x|+|y| for real numbers x and y

#math,#algebra,#proofs,numbers,integration,differentiation,derivative,integral,math elite,mathelite,maths,mathematics,calculus

[MathElite]

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[AnmolTheMathSailor]

Ohh wow wow wow congratulations for 800 subscribers . I wish my best I could write congratulations for 1k soon for you ❤

[p_square]

There are 2 proof other than yours :
1. a^2 + b^2 + 2|a||b| >= a^2 + b^2 + 2ab
(|a|+|b|)^2 >= |a+b|^2 (x ∈ R; x^2 = |x|^2)
=> |a|+|b| >= |a+b|

2. We can prove it by using the definition of the absolute value wherein we first establish that |x| = max{x, -x} and +-x =< |x|. Then you can use the fact that a+b =< |a|+b =< |a|+|b| and
-a-b =< |a|-b =< |a|+|b|

However, your proof was short and concise. Also, good luck with the bprp challenge

[MathZoneKH]

Congratulations for more than 800 subs sir

[mathevengers]

As you have taken part in bprp's challenge, when are you going to make a video on your introduction and your goal?

[mohamedihab]

Good and short proof, great, Math Elite.

[vedants.vispute]

OMG we were learning inequalities and especially I learnt this today and this video got me recomended!

[chauhan.]

Can it be possible for any value of a real number z such that |x + y + z| ≤ |x| + |y| + |z|?!?

[mathevengers]

I have a question related to bprp's challenge. I asked this question in his last two videos but he didn't answer. The question is what if during the 3 months duration the number of subscribers increases and gets 3000? Will he be still eligible or get eliminated? What do you think?

[akshatjangra]

Imagine you make a very good video and gain 3k subscribers and become ineligible for the bprp Have Won But At what cost?350?