What is the Value of u(t) at t=0? - Ingyil

[Ingyil]

Hi.
I want to know what you think about this, that's why I write this message.
According to the function u(t):

____ | 1, t>0
u(t)=| ?, t=0
____ | 0, t<0

What do U think about the value of the function u(t) when time is 0?
Is it define? or not?
Some books say that the value is 1, but others don't.
According to general knowledge in books, what do they say? What do you think?

Bye.

Ingyil.

 

[mathwonk]

As you presented it, it is not defined at t = 0, simply because you did not say what the value is at 0. I.e. whether or not it is defined is not a god given property of a function, it is entirely up to you, and you chose not to define it at 0.

However, once that is said, we enter upon the question of whether there is some one "best" way to define this function at 0.

A favorite condition is to ask whether the function can be defined at 0 to become continuous there, and if that were true, there would be only one way to do it.

In this case however, the function you defined has different limits as we approach 0 from both sides, hence it cannot be defined so as to be continuous.

You can make it "continuous from the right" by defining it to be 1 at 0, and you can make it "continuous from the left" by defining it to be 0 at 0.

does this help?

 

[arildno]

Another "good" choice is to define u(0)=1/2 (some approximations to this functions would like this value..)

However, as it stands, the function is simply not defined at t=0, and you should accept that; and as mathwonk says, there exist no way of finding the function's "true" value there, that "quest" is basically meaningless.