When creating a vector why does the size change when using a variable vs using a value?

I am trying to create the time vector that starts at 0, has a step size of variable predefined (stepsize) and ends at predefined variable (fin_time).

In this case I calculated stepsize=0.0990 and fin_step=14.256

It would look like this time=[0:stepsize:fin_time]. When I type this I get a 144x1 vector.

When I type the value of stepsize manually. time=[0:0.0990:fin_time] I get a 145x1 vector. This is what I want.

How come the variable is exactly the same value but gives a different answer?

Answer 1

[Stephen23]

"How come the variable is exactly the same value but gives a different answer?"

No, the values are not exactly the same.

In one case you calculate the value, in the other case you write it explicitly. These are not the same value, but you forgot to actually check this using any reliable method (e.g. num2strexact, format hex, etc).

Read more about binary floating point numbers:

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal

http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug

http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab

This is worth reading as well:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf