logic

I was trying to prove the following simple theorem from an online course that excluded middle is irrefutable, but got stuck pretty much at step 1: Theorem excluded_middle_irrefutable: forall (P:Prop), ~~(P \/ ~ P). Proof. intros P. unfold not. intros H. Now I get: 1 subgoals P : Prop H : P \/ (P -> False) -> False ______________________________________(1/1) False If I apply H , then the goal would be P \/ ~P , which is excluded middle and can't be proven constructively. But other than apply , I don't know what can be done about the hypothesis P \/ (P -> False) -> False : implication -> is

I've heard that it's possible to accomplish this using the modulus % operator present in most programming languages. The real question is, how? I'm unfamiliar with how modulus works, so I've had difficulties using it in the past. Given the present time here in seconds since 1970, 1307758473.484 , how can I calculate how many years that is, days that is, hours that is, and minutes that is using modulus? I'm essentially looking to format it like this: "5 years, 10 days, 12 hours, 7 minutes, and 18.56 seconds". How would I do this? I'm really interested in learning the logic behind this and not

I'm super excited about my program powering a little seven-segment display, but when I show it off to people not in the field, they always say "well what can you do with it?" I'm never able to give them a concise answer. Can anyone help me out? flolo First: They don't need to have volatile memory. Indeed the big players (Xilinx, Altera) usually have their configuration on-chip in SRAM, so you need additional EEPROM/Flash/WhatEver(TM) to store it outside. But there are others, e.g. Actel is one big player that come to mind, that has non-volatile configuration storage on their FPGAs (btw. this

Write C/C++/Java code to convert given number into words. eg:- Input: 1234 Output: One thousand two hundred thirty-four. Input: 10 Output: Ten Does it require a complete switch case for digits 0 to 10. Adding "teen" after every number name (eg: 14: four "teen".) from 14 to 19. And than adding "ty" and the digits name for a number in the range 20 to 99. And so on. I think there must be some far better approach for solving this. C code is preferred. pr6989 #include<iostream> using namespace std; void expand(int); int main() { int num; cout<<"Enter a number : "; cin>>num; expand(num); } void

I have an Event table that specifies a date range with start_date and end_date fields. I have another date range, specified in code, that defines the current week as 'week_start' and 'week_end'. I'd like to query all Events for the week. The cases seem to be: Event begins and ends within the week Event begins before the week, but ends within the week Event begins within the week, but ends after the week Event begins before the week and also ends after the week Events that neither reside within, nor overlap the week at all are ignored I'm attempting to come up with a query that can handle all

In problem 4 from http://projecteuler.net/ it says: A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 * 99. Find the largest palindrome made from the product of two 3-digit numbers. I have this code here def isPalindrome(num): return str(num) == str(num)[::-1] def largest(bot, top): for x in range(top, bot, -1): for y in range(top,bot, -1): if isPalindrome(x*y): return x*y print largest(100,999) It should find the largest palindrome, it spits out 580085 which I believe to be correct, but project euler doesn't think