This is really a basic question:
Let's say we have a message that is sent 2 times each second (periodic message). Thus, we can say that each 0.5s we send a message. But I am trying to understand it in an intuitive way. Let me be more clear about it: if for at instant t=0s, we send a message, than we wait 0.5s we send another message, thus we have sent 2 messages in 0.5s which contradict my hypothesis, further more if we continue to send at t=1s, we can say that we sent 3 messages in 1s.
What is wrong with this reasoning?
Thank you.
First of all, sending two messages a second doesn't imply that they have to be sent at equally spaced intervals. But that aside, the error in your reasoning stems from the fact that you're being a little sloppy with the notion of an interval.
If we model time with the real numberline then your intervals are the following: [0,1), [1,2), [2,3), ... And your signal time-stamps are t=0, t=0.5, t=1, t=1.5, t=2, ... Now you can see that you have two signals per second, without any contradiction.
Note that 0 and 0.5 belong to the first interval, 1 and 1.5 belong to the second interval, etc.