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Mendicant_Bias
 one year ago
(Introductory Real Analysis) I'm trying to transform a given expression with absolute value signs into a version without it by applying the formal definition of the absolute value function (example below), but I'm running into trouble when I get more than one absolute value sign inside another.
Mendicant_Bias
 one year ago
(Introductory Real Analysis) I'm trying to transform a given expression with absolute value signs into a version without it by applying the formal definition of the absolute value function (example below), but I'm running into trouble when I get more than one absolute value sign inside another.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i could see how that would be annoying

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1(Sorry, just having trouble putting up the LaTeX, I'll try to put up a pic instead of the math maybe)

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1How do I do a piecewise function bracket again? I'm trying to do it, but am somewhere making a mistake.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me do one, you can copy it

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1I'm trying this: \begin{displaymath} f(x) = \left\{ \begin{array}{lr} 1 & : x \in \mathbb{Q}\\ 0 & : x \notin \mathbb{Q} \end{array} \right. \end{displaymath} to display the abs. value function, and it's not rendering

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x) = x+4 = \left\{\begin{array}{rcc} x + 4 & \text{if} & x \geq 4 \\  x  4& \text{if} & x < 4 \end{array} \right.\]

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1What the hell? I just typed it all up in the equation box, and when I entered, nothing was there. OS isn't playing nice with me atm.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[f(x) = \left\{\begin{array}{rcc} 1 & \text{if} & x \in\mathbb{Q} \\ 0& \text{if} & x\notin\mathbb{Q} \end{array} \right.\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not really an absolute value equation though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0or function or whatever

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[ f(x) = \left\{ \begin{array}{lr} 1 & : x \in \mathbb{Q}\\ 0 & : x \notin \mathbb{Q} \end{array} \right.\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is what you wrote i just omitted the "displaymath" in favor of \[

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2i smell a continuity/discontinuity proof is on the way

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.0I think sense they are working with the definition of absolute, they will be doing stuff like triangle inequality, and results of it :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Mendicant_Bias you know how to copy this right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh i thought it would be something like \[f(x)=x+32\]

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1...And now it is, nevermind, just tremendous lag/delay between it rendering.

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.0What are you trying to do with it, most of the time we don't use the definition.

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1I'm trying to change the expression to not have the absolute value signs, which I did by using (max) and (min). http://i.imgur.com/l7T5TkD.png

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441165013039:dw

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1What I did was simplify the insides and then use max on this one, e.g. \[a+b+ab=2 \ \text{max}(a,b)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0course the first one is \(2a\) and the second is \(2b\)

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1\[a+b+2x+ab+a+b2c+ab\] I'd in principle, like to do the same thing, but I don't know what will happen/how the absolute value inside another one will work, really.

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1Whoops, no x, that's c.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah was afraid of those nested absolute values

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\(a\gt b\) : \[a+b+2x+ab+a+b2c+ab \\= a+b+2x+ab + a+b2c+ab\\=2a+2x + 2a2c\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2you just follow the rules but what exactly is the actual problem

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1"Write the following expressions in equivalent forms not involving absolute values."

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2ahh that really going to require some clever thinking..

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1Do you have to do it recursively, then? e.g. are there four possible outcomes or something like that, or do you just take the same condition you first applied to the outside absolute value signs and apply it again? Yeah, and I've never actually seen or used the max/min(value, value, value...) notation, came up unexpectedly.

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1But yeah, x is actually c, typo

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\(a\gt b\) : \[a+b+2c+ab+a+b2c+ab \\= a+b+2c+ab + a+b2c+ab\\=2a+2c + 2a2c\\ = 2max(a,c)\]

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1Guessing you just apply the same logic of the last problem after the first abs. val sign is gone

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes looks its similar..

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1Alright, cool. Gonna play with this for a second, but I think I got it.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2does this work ? \[a+b+2c+ab+a+b2c+ab \\~\\ = 2max(a+b+ab, ~2c)\\~\\ = 2max(2max(a,b), 2c) \]

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1Wow, this is kind of bizarre. I don't know if I just haven't noticed something like this in math yet, but I don't think I've ever noticed something that feels like an operation/changing something (e.g. a>b) and it influencing an expression in layers all at once without having to break them down to get to the "inside" layer. It's not really math, it's an assumption, but I'm so used to order of ops. problems that having something change like that seems strange. The answer is a little different, and a little more aesthetically pleasing, if that's a hint, heh

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1Think I got it, one sec. http://i.imgur.com/V1jKffw.png Now turning that into max/min things.

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1Yeah, it's just \[4 \ \text{max(a,b,c)}\] Yeah, hah

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1Has a ring to how it's written. Well, cool! Thanks so much for helping me figure this out! I definitely wouldn't have gotten it had I not asked...lol

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1I didn't know that max worked like that, awesome.

Mendicant_Bias
 one year ago
Best ResponseYou've already chosen the best response.1(I mean, I didn't know how max worked at all a couple of hours ago, heh)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2they are usually messy the given expression was cooked up to work out smoothly haha

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[\color{blue}{a+b+ab}+\color{red}{2c}+\color{blue}{a+b+ab}+\color{red}{2c} \\~\\ = 2max(\color{blue}{a+b+ab}, ~\color{red}{2c})\\~\\ = 2max(\color{blue}{2max(a,b)}, \color{red}{2c})\\~\\ =4max(\color{blue}{max(a,b)},c)\\~\\ =4max(a,b,c) \]
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