Why is any number (other than zero) to the power of zero equal to one? Please include in your answer an explanation of why $0^0$ should be undefined. 0.0.0.0 means that any IP either from a local system or from anywhere on the internet can access. It is everything else other than what is already specified in routing table. What does the \0 symbol mean in a C string? It's the end of a string. A null character. In memory, it's actually a Zero. Usually functions that handle char arrays look for this character, as this is the end of the message. I'll put an example at the end. What is the length of str array? (Answered before the edit part) 7 and with how much 0s. %0 references argument 0 – the name of the batch file – always exactly as specified on command line or in another batch file. So if a batch file named Test.bat stored in C:\Temp is started for example from within a command prompt window with current directory being C:\ with an execution of temp\test, then %0 is substituted by temp\test on execution of the batch file. But %~f0 is. Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? It seems as though formerly 0 0 $0$ was considered in the set of natural numbers, but now it seems more common to see definitions saying that the natural numbers are precisely the positive integers. Generally the only reason one sees 1/0 as infinity is because some systems (incorrectly) output infinity when given dividing by zero. As we all know the IPv4 address for localhost is 127.0.0.1 (loopback address). What is the IPv6 address for localhost and for 0.0.0.0 as I need to block some ad hosts. I don't feel like I proved much here, all my life I took for granted that 0x = 0 0 x = 0 $0x=0$ was obvious but I really never even thought of questioning why that is so. I want to get ahead and learn the basics of Analysis before taking a course on it so I am looking to get basic facts right before moving on to the good stuff. Thus, to see if I understand the concept of a field − − $-$ I. \0 is the NULL character, you can find it in your ASCII table, it has the value 0. It is used to determinate the end of C-style strings. However, C++ class std::string stores its size as an integer, and thus does not rely on it. @Arturo: I heartily disagree with your first sentence. Here's why: There's the binomial theorem (which you find too weak), and there's power series and polynomials (see also Gadi's answer). For all this, 00 = 1 0 0 = 1 $ 0 ^ 0 =1$ is extremely convenient, and I wouldn't know how to do without it. In my lectures, I always tell my students that whatever their teachers said in school about 00 0 0.