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 (A ∧ B) ∨ A This is equivalent to just 'A', but I can't remember how to simplify that out of it. Hints, please? : ) [Quote] [Link]
 Blake Webmaster2083 Posts11 Cado 14:3 - 6.80.51636.143 days ago If B is true, then the "AND B" is a no-op and you're left with "A OR A" which is just A. If B is false, then "(A AND B)" is false and "(A AND B) OR" is a no-op, leaving A. You mean like that? Or is there a specific theorem name you're looking for? [Quote] [Link]
 Well I checked it by exhaustion which is a sufficient proof, but I was looking for an algebraic simplification.  Something from http://en.wikipedia.org/wiki/Propositional_calculus#Basic_and_derived_argument_forms can probably do it. Haven't read the whole list yet. [Quote] [Link]
 Blake Webmaster2083 Posts11 Cado 14:3 - 8.60.9636.053 days ago It's called absorption. http://en.wikipedia.org/wiki/Boolean_algebra_%28logic%29#Axioms [Quote] [Link]
 Hydrogen777 Administrator5988 Posts11 Cado 14:3 - 9.56.64636.005 days ago Since absorption is an axiom, you shouldn't have to prove it symbolically. In fact, I'm not sure you can prove it just using other axioms. A truth table should suffice. [Quote] [Link]
 I was trying to prove to myself that I had rewritten this code   function futureUnpaidInvoices() : List{     var invoices = this.InvoicesSortedByDate.where(\ inv ->              (               inv.InvoiceItems.Count > 0 or                inv.ManualInvoice             ) and             (               inv.PaidStatus != TC_FULLYPAID and                inv.InvoiceItems.Count > 0             ) and             (               !inv.InvoiceItems.hasMatch(\ii->ii.DownPaymentBool)             )                            ).toList()      return invoices   } correctly into this -   function futureUnpaidInvoices(includeDown : boolean) : List{     var selectSOMEofTheTHINGS = \ inv:Invoice ->              ( inv.InvoiceItems.Count > 0 or inv.ManualInvoice ) and // legit             ( inv.PaidStatus != TC_FULLYPAID ) and // pending or outstanding             ( includeDown or !inv.DownPayment ) // no downs unless requested                   return this.InvoicesSortedByDate.where(selectSOMEofTheTHINGS).toList()   } Turns out my change is correct, so that's nice to see. It's also nice to find out the reason I couldn't derive the result I wanted was because that transformation is axiomatic. We had what I thought was a pretty good coverage of Boolean algebra in CS301 but I don't remember ever seeing the absorption axiom before. I think I'm going to go read that article in detail. [Quote] [Link]
 Two things. 1. I've seen it explained elsewhere, but not well. Can anyone show the formula for 2+2=5? 2. Another toughie. Can anyone explain 4th dimensional figures. And don't just link to a Wikipedia article, I mean an actual explanation. I'd appreciate it! Thanks! [Quote] [Link]
 The first is a reference to George Orwell's novel 1984. I'd need to know exactly what you're referring to with regards to the second if you want an actual answer. Are you interested in contour plots or what? Otherwise, I just suggest you wait until multivariable calculus before you start considering higher dimensions. [Quote] [Link]
 For 2, something along these lines. Number one I've seen done places. It's weird. I DO know the reference. [Quote] [Link]
 With regards to number one, you've seen it done incorrectly. Well, with regards to the math, you basically treat it the same way as any number of other dimensions in standard Euclidean space. It doesn't really matter if it's 4 dimensions or 400 dimensions. One's just less work. As far as expressing a four dimensional object in fewer dimensions, think of a contour plot or topographic map. The image you see is a represntation of it in fewer dimensions. Here's an interactive example. Basically, the way level sets work is you keep one value constant and then draw what you have from there. So, as you vary one value, the object will appear to be shifting when it is, in fact, not. I'll go see if I can find an interactive example of that. (Note, this doesn't seem to work for me, but it might for you) [Quote] [Link]
 ndm2271 Posts11 Abeo 0:4 - 9.52.64629.007 days ago I think I sort of get #2. Thanks. As for one: http://www.warriorforum.com/off-topic-forum/52565-proof-2-2-5-a.html That's where I first found it. [Quote] [Link]
 Hydrogen777 Administrator5988 Posts11 Abeo 0:4 - 11.56.27628.905 days ago That "proof" isn't even syntactically correct, let alone mathematically correct. [Quote] [Link]
 You can find a slightly better attempt debunked a few threads down, in the "4=5" thread. [Quote] [Link]
 ∏=3.141592653589793238462643383279502884197169399375105820974944592307816406286 that's all I know. [Quote] [Link]
 Hydrogen777 Administrator5988 Posts12 Ineo 0:1 - 16.14.12626.676 days ago That was incorrect. [Quote] [Link]
 The pi thing? It's correct, isn't it? EDIT: Unless you mean he/she didn't specify the amount of decimal places and that 22/7 would be a better answer. [Quote] [Link]
 How would I solve for x? I've tried it a few times but I can't get the answer which is 3. The red L is just the question number. [Quote] [Link]
 Multiply both sides by 18. This will eliminate the fractions. From there, distribute the the coefficients into your parenthesized terms. After that you isolate the x onto one side. From there, you just divide out the coefficient. Hint: You're trying to get to 3. [Quote] [Link]
 Hydrogen777 Administrator5988 Posts12 Ineo 0:1 - 17.70.83626.597 days ago Dread said:The pi thing? It's correct, isn't it? EDIT: Unless you mean he/she didn't specify the amount of decimal places and that 22/7 would be a better answer.Pi is not expressible as a decimal number - it can only be approximated. [Quote] [Link]