U r right but u should add one more step at the end X^2>y^2 THEN WE CANT say directly that x>y it is mathematically incorrect Correct statement is |x|>y it means xy So, here |a|+|b||a+b| But |a|+|b| is always positive so first one is wrong so, |a|+|b|>|a+b|
Hi Math Sorcerer: Could u explain the following? Prove Lim x tends to infinity 4x2-3x+2/8x2-6x+1 =1/2 Tried to understand it with the help of someone else, it’s difficult to clearly understand. Thank you
Interesting video> Can you prove it with the axioms O1-O5? That's what I have the most trouble with. Also can you prove the triangle inequality geometrically? I'm in first year math, so I have a ton to learn!!! Thanks for the video.
at 02:36 if you take the square root of an inequality shouldn't you take into consideration also the possibility of abs(a) + abs(b) =9 x could be greater than 3 but it could also be smaller than minus 3.
Great video! What happens with the +/- when you take the square root at the end?
5 лет назад+1
He is using a property of the absolute value which states that, for a real number x, the absolute value of x equals the square root of x squared " |x|=(x^2)^(1/2) ". When he takes the square root, he is doing the square root of a squared number, so it is therefore equal to the absolute value of that number, and because that number is positive you can forget about the absolute value.
*thANK you* I was look for this in the textbook and I was just confused what they were referring to The Math Sorcerer comes to the rescue once again! :)
+The Math Sorcerer Wow! It took me so long to get this annoying inequality! I shall be forever thankful. As I noticed, the tricky part was at the 2|ab| ≥ 2ab.
I understood the proof as you showed it, but I just really wanted to know in which cases |a| + |b| > a + b, because as far as my small brain can imagine, they are always equal.
@@user-qw4vg9lf5v What if either a or b is negative. Then a+b will always be smaller than positive a + positive b (i.e., |a|+|b|). Draw a number line. Take a look. Also, -a+-b is always smaller than a+b since it is to the left of a+b. Any number to the left of a number is always smaller.
If somebody tell her or his life got ruin, what about the unbreakable mind. If only one part of your body, soul or psyche are heal, you can build your whole body, soul and psyche healed like that only part as building ground spot. Identity analyses can be for more reasons than narssissmic personality. Or to find some great in you. It can be the oposite, to discover what have make you miserable. The first result isnt always the right.
I've been watching the playlist and I'm learning a lot from these videos. I'm new to this and am just learning it on my own. I was wondering if the following is a valid proof: |a+b| = |a+b + b/2 - b/2|
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thank you so much! I was so discouraged when my teacher just told me to memorize this property. Thanks for helping me out!!!
I believe you still need to look at three cases: a and b have different signs; a and b are positive; a and b are negative.
This series is incredibly helpful and well-explained.
Subscribed.
U r right but u should add one more step at the end
X^2>y^2 THEN WE CANT say directly that x>y it is mathematically incorrect
Correct statement is |x|>y it means xy
So, here |a|+|b||a+b|
But |a|+|b| is always positive so first one is wrong so, |a|+|b|>|a+b|
Quick and straight forward, nice. Subscribed!
You just expanded it and then recondensed it? What was proven
That's how they behave 😂
Wow ! ... Wake up
I think you didn't understand clearly. IMHO.
It was a good proof what you on?
Thank you .
I was seriously about to drop my Advanced Calculus class .
Hi Math Sorcerer:
Could u explain the following?
Prove
Lim x tends to infinity
4x2-3x+2/8x2-6x+1
=1/2
Tried to understand it with the help of someone else, it’s difficult to clearly understand.
Thank you
short, straightforward, nice done indeed
Wow, this is really ingenious! Thank you for making this video!
You are welcome!
Thank you! You explained better than my textbook did!! I am new to your channel and saw this vid and subscribed! Thanks, Sorcerer!!!
Super helpful thank you!!! Quick, clear, and easy to follow!
when proving 2ab
Very nicely done. Thank you so much!
Thank you so much for posting this!
Interesting video> Can you prove it with the axioms O1-O5? That's what I have the most trouble with. Also can you prove the triangle inequality geometrically? I'm in first year math, so I have a ton to learn!!!
Thanks for the video.
you deserve more views :)
:)
it helped me so much..thank you
at 02:36
if you take the square root of an inequality shouldn't you take into consideration also the possibility of
abs(a) + abs(b) =9
x could be greater than 3 but it could also be smaller than minus 3.
what about doing this case by case in terms of whether a and b are positive/negative??
What about not doing that
@@triton62674 what about not doing this and that
You can do that too. That requires 3 cases. But I don't think that's suitable to do in an exam. That might take longer unless you have a lot of time.
I did this in my exam and my teacher didn't give full marks. I got 2/5.
why?
😂😂
Grazie mille per questo video, short e anche facile da capire
When you square root both sides, does this not create multiple solutions with negative roots? Anyways great video!
Up
Great video!
What happens with the +/- when you take the square root at the end?
He is using a property of the absolute value which states that, for a real number x, the absolute value of x equals the square root of x squared " |x|=(x^2)^(1/2) ". When he takes the square root, he is doing the square root of a squared number, so it is therefore equal to the absolute value of that number, and because that number is positive you can forget about the absolute value.
Thanks in advance. Could we generalize triangle inequality for polygens?
You're the most recent comment so im going to ask u, Just because /a/ is >= a and for b does the equation change from = to >=?
This is one concise explanation and it,s not even the best part about it😅. Thank you
Many thanks for this good video.
👍
Beautiful!!!
Both values are equal ... How ?
Please give one example
can you tell me how to derive this inequality from the orignal inequality in the video ------> |a-b|>= |a|-|b|
Perfect demostration im in first of industrial engeneer and it is helpful
awesome!!
It bothers me that in the Grammarly ad, ShakesPeer was never corrected and the narrator still said "much better".
Ikr
Well explained. The proof I read doesn't even come to this conclusion
*thANK you* I was look for this in the textbook and I was just confused what they were referring to
The Math Sorcerer comes to the rescue once again! :)
Nice work 🎉
thanks ,,,helpfull
np:)
Thank you so much, now I understand.
+The Math Sorcerer
Wow! It took me so long to get this annoying inequality! I shall be forever thankful.
As I noticed, the tricky part was at the 2|ab| ≥ 2ab.
יהודה שמחה ולדמן
glad it helped!!
Nice!!!
Nice video 🤗but can't able to see clearly
what ! i am crying. thank you sm for this
Good 👍
Thanks. A lot 👍
Thhhank you very much finally I am understand will 😩💜
How to find proof goal.plz ans this question..?
Can you help with a question please?
I understood the proof as you showed it, but I just really wanted to know in which cases |a| + |b| > a + b, because as far as my small brain can imagine, they are always equal.
Because a+b>-(a+b)
@@user-qw4vg9lf5v What if either a or b is negative. Then a+b will always be smaller than positive a + positive b (i.e., |a|+|b|). Draw a number line. Take a look. Also, -a+-b is always smaller than a+b since it is to the left of a+b. Any number to the left of a number is always smaller.
wtf, why is my profs proofs so much harder than this. It uses cases showing that X+Y
Wait, what? 🤯
If somebody tell her or his life got ruin, what about the unbreakable mind. If only one part of your body, soul or psyche are heal, you can build your whole body, soul and psyche healed like that only part as building ground spot. Identity analyses can be for more reasons than narssissmic personality. Or to find some great in you. It can be the oposite, to discover what have make you miserable. The first result isnt always the right.
nice!
not understanding at 1:35 how does it go from being equal to being greater than or equal to ?
it's because |a| >= a and |b| >= b, so you can drop the | | and insert >=
@@TheMathSorcerer ah I see, thank you 🙇♀️
The Math Sorcerer why is |a|>=a and |b|>=b?
Elyne Khoo because a and b can be intrinsically negative but absolute value is always positive
@@elynekhoo if you don't know this, then you do not know what absolute value means.
nice
Jiri would never
10/10 proof
Jiri sux
Yeah, but actually no.
I've been watching the playlist and I'm learning a lot from these videos. I'm new to this and am just learning it on my own. I was wondering if the following is a valid proof:
|a+b| = |a+b + b/2 - b/2|
No, because you are already assuming that the Triangle Inequality is true when you wrote |a+b + b/2 - b/2|
Watch out the thumbnail the vedio was different
(a+b)2 does not equal |a+b|2 .... why is no one saying anything ...
for all real numbers x it is true that |x|^2 = x^2, a + b is a real number, therefore |a+b|^2 = (a+b)^2
Hi
Can you prove this
0 < x < 1 ⇒ 0 < x^2 < x < 1
Hi
Hi
Frick Jiri
What? I'm confused. What are we going to prove ? 😳
Skipped too many steps. This is a quick and dirty proof, but not a whole proof.