The Forum > Math & Science > Math Problem Thread

Well I checked it by exhaustion which is a sufficient proof, but I was looking for an algebraic simplification. [Edit] 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. |

I was trying to prove to myself that I had rewritten this code function futureUnpaidInvoices() : List<AccountInvoice>{ correctly into this - 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 } function futureUnpaidInvoices(includeDown : boolean) : List<AccountInvoice>{ 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. |

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. |

For 2, something along these lines. Number one I've seen done places. It's weird. I DO know the reference. |

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) |

The Forum > Math & Science > Math Problem Thread