# Squaring

Watch
Announcements
Thread starter 5 years ago
#1
If (a^2 + b^2)^1/2 = c then why doesn't a + b = c ?

Posted from TSR Mobile
0
reply
5 years ago
#2
1
reply
5 years ago
#3
Should say provided a or b aren't 0 at the bottom

Posted from TSR Mobile
0
reply
5 years ago
#4
(Original post by maths_4_life)
If (a^2 + b^2)^1/2 = c then why doesn't a + b = c ?

Posted from TSR Mobile
^^ i think this is what you're assuming
0
reply
5 years ago
#5
From your first identity

From your second identity

Which would imply for both of your identities to be equal, a or b must equal 0. Otherwise they are never equal
0
reply
5 years ago
#6
(Original post by thefatone)
^^ i think this is what you're assuming
I'm assuming both statement are equivalent to show that a contradiction arrives from this equivalency, which is 2ab=0, which cannot be true unless a and or b =0,

Posted from TSR Mobile
1
reply
5 years ago
#7
oh ok

(Original post by drandy76)
I'm assuming both statement are equivalent to show that a contradiction arrives from this equivalency, which is 2ab=0, which cannot be true unless a and or b =0,

Posted from TSR Mobile
0
reply
5 years ago
#8
(Original post by maths_4_life)
If (a^2 + b^2)^1/2 = c then why doesn't a + b = c ?

Posted from TSR Mobile
The other users have provided you with perfectly valid proofs so I'm not going to go on with that, I'll give a few counter examples (remember, testing out special cases is always a good way of making sure what you're writing down is correct) and then go on and talk/waffle on a bit about something called linearity. I'm going to write in a very informal and unrigorous way that is meant to supplement your intuition, so nobody hate on me.

Okay - first off, try and drill the practice of checking special cases in your head as you write something down. So if you're writing try and practice to get your head to test the case for example.

It's fairly obvious that right away this gives you but it is not the case that so that should set off alarm bells right away.

Okay, now onto me waffling about linearity: so things are linear when they satisfy (amongst other things) the fact that , it's quite a privilege to work with linear things, it makes life very easy.

A few examples of linear things is, well... a straight line, is linear because , makes life very easy, you don't need to worry about stuff so much.

Another example of linear things is integration or differentiation, although we're moving away from the realm of functions and into the realm of operators here (this needn't concern us, though) we can call differentiation linear because - see, life is easy! We don't need to worry about whether we add then differentiate or differentiate and add, meh, it all works out to be the same thing.

Okay, linear is easy... that kinda makes nearly everything not being linear kinda make sense, because when is maths easy, eh? Functions, in general aren't linear. isn't a linear function, unfortunately. I've just said that square rooting isn't a linear function! So it does not hold that .

In general, square rooting is a messy business, it works from (we're constraining ourself to the reals here, it we want to go complex, bleurgh), we need to take care of the signs, restrict our domains, makes sure to use moduli bars, etc... so it hardly stands to reason that square rooting is going to be linear and make life easy for us, oh no, that's not what little Mr. Square Root is going to do. He's going to stand there and make life hard.

Square rooting and logarithiming (made that word up, hi) kind of provoke the same reaction in me, whenever I see or I know right away I can split that up into or and make life easy, but as soon as I see or , I close my eyes and go cry a little bit because there's nothing I can really do now!

So, hopefully, that mildly entertaining drivel has let you intuit that .
0
reply
5 years ago
#9
(Original post by Zacken)
X
0
reply
5 years ago
#10
(Original post by Student403)
...
Dying.
0
reply
5 years ago
#11
(Original post by Zacken)
Dying.
Dude I legitimately think you're better at maths than my teachers
0
reply
5 years ago
#12
(Original post by Zacken)
x.
the absolute value of 3 is 3, and the absolute value of −3 is also 3.<---- i don't understand this bit can you explain pls?
0
reply
5 years ago
#13
(Original post by thefatone)
the absolute value of 3 is 3, and the absolute value of −3 is also 3.<---- i don't understand this bit can you explain pls?
I like to think of the absolute value as the distance from the origin

Posted from TSR Mobile
0
reply
5 years ago
#14
(Original post by drandy76)
I like to think of the absolute value as the distance from the origin

Posted from TSR Mobile
i don't quite understand that either....
0
reply
5 years ago
#15
(Original post by thefatone)
i don't quite understand that either....
-3 is 3 units away from 0
3 is also 3 units away from 0
0
reply
5 years ago
#16
(Original post by thefatone)
the absolute value of 3 is 3, and the absolute value of −3 is also 3.<---- i don't understand this bit can you explain pls?
We define the absolute value function:

So plug in into the function we get that since so we take the top bit of the definition:

Plug in into the function we get that since so we take the bottom bit of the definition .

Essentially, the absolute value functions strips away the sign of the number and makes it positive.

Because the absolute value function is defined piecewise, it stands to reason why it is not differentiable at its cusp, more specifically: so the derivative is undefined for and that is because it is undefined there.

Most of this post is useless extra knowledge, but... meh.
0
reply
5 years ago
#17
(Original post by Student403)
-3 is 3 units away from 0
3 is also 3 units away from 0
oh that makes sense....

so ± are interchangeable?
0
reply
5 years ago
#18
(Original post by Zacken)
We define the absolute value function:

Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
\displaystyle

\begin{equation*} |x| = \begin{cases} x \quad \text{for } \, x \geq 0 \\ -x \quad \text{for } \, x &lt; 0\end{cases}\end{equation{*}

So plug in into the function we get that since so we take the top bit of the definition:

Plug in into the function we get that since so we take the bottom bit of the definition .

Essentially, the absolute value functions strips away the sign of the number and makes it positive.

Because the absolute value function is defined piecewise, it stands to reason why it is not differentiable at its cusp, more specifically: so the derivative is undefined for and that is because it is undefined there.

Most of this post is useless extra knowledge, but... meh.
seems pretty dangerous... do i learn this in c3 and c4?
0
reply
5 years ago
#19
(Original post by thefatone)
oh that makes sense....

so ± are interchangeable?
I wouldn't put it that way - Zain explains it well
0
reply
5 years ago
#20
(Original post by Student403)
I wouldn't put it that way - Zain explains it well
ok
0
reply
X

Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### Poll

Join the discussion

#### If you haven't confirmed your firm and insurance choices yet, why is that?

I don't want to decide until I've received all my offers (3)
60%
I am waiting until the deadline in case anything in my life changes (1)
20%
I am waiting until the deadline in case something in the world changes (ie. pandemic-related) (1)
20%
I am waiting until I can see the unis in person (0)
0%
I still have more questions before I made my decision (0)
0%
No reason, just haven't entered it yet (0)
0%
Something else (let us know in the thread!) (0)
0%

View All
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.