- #1
Nader AbdlGhani
- 38
- 2
What's the difference between [tex]f(x)=3[/tex] and [tex]f(x)=3x^0[/tex] ? and why Limit of the second function when [tex]x\rightarrow0[/tex] exists ? and is the second function continuous at [tex]x=0[/tex] ?
jedishrfu said:Here's a fun discussion on the 0^0 from the perspective of students, teachers, and mathematicians:
http://www.askamathematician.com/20...ematicians-and-high-school-teachers-disagree/
Maybe it's not. But I also think it's natural, simply for the reason that taking something to a power is something multiplicative. And therefore it makes sense to define it as the unit 1.micromass said:I disagree very much with the mathematician's explanation. They're like saying that ##0^0 = 1## is a consensus among mathematicians, it's not.
fresh_42 said:Maybe it's not. But I also think it's natural, simply for the reason that taking something to a power is something multiplicative. And therefore it makes sense to define it as the unit 1.
micromass said:Sure, there are plenty of reasons why it should be ##1##. The best are set theoretic and category theoretic. But there is no consensus.
Binary? What about defining 00 as the limit $$\lim_{x \to 0} x^{1/\log(x)} = e$$? You can also get every other number of course.jedishrfu said:At least its a very binary decision and mathematicians can wear the shirt:
mfb said:Binary? What about defining 00 as the limit $$\lim_{x \to 0} x^{1/\log(x)} = e$$? You can also get every other number of course.
fresh_42 said:The vast, boring, senseless, stupid, Sisyphus-like, unprofitable and endless job to rewrite formerly beautiful and nice formulas like, e.g.
$$\exp(x) = \sum_{n = 0}^{\infty} \frac{x^n}{n!}$$
is justification enough for the choice of ##1##.
A function is a block of code that performs a specific task and can be called from anywhere in a program. A method is a function that is specific to an object or data type and can only be called on that object or data type.
Both a function and a subroutine are blocks of code that can be called from other parts of a program. They both can accept input parameters and return an output result.
A built-in function is a function that is already defined and included in a programming language, while a user-defined function is created by the programmer to perform a specific task.
A function returns a value as a result of its execution, while a procedure does not return a value. Procedures are typically used for tasks that do not require a return value, such as printing or displaying information.
A function is a named block of code that can be called from anywhere in a program, while a lambda expression is an anonymous function that can be used as a parameter or assigned to a variable. Lambda expressions are typically used for simpler, one-time tasks.