If one was to separate [0,4] into four equal sets, what would the correct notation be?

Question

If one was to separate [0,4] into four equal sets of positive real numbers, would the result be:

[0,1), [1,2), [2,3), [3,4)

or

(0,1), (1,2), (2,3), (3,4)

or something else?

Answer 1

Four Congruent Parts

Based on the comments, it seems that one possible intended/desired meaning of "equal" is (geometrically) "congruent" (in the sense that each part can be reflected and/or translated to become exactly the same another part).

For that meaning, the answer is that it can't be done. But I don't think that's at all obvious. I cite Partitioning an Interval Into Finitely Many Congruent Parts by William Gustin. Basically, he proves that for a problem that's at all like this: if it can be done, then it can be done with intervals. And as the OP basically notes, it's clear it's impossible to break $[0,4]$ into four congruent intervals.

Four Parts of the Same Cardinality

As noted by another Mark in the comments, a partition such as $\left\{[0,0.001], (0.001,\frac12), [\frac12,0.7), [0.7,4]\right\}$ would have four parts of the same cardinality.

Four Parts of the Same "Length"

In measure theory, the concept of "Length" is generalized to "lebesgue measure", which generally agrees with total length any time you would have intuition about length. The measure/length is the same for a closed interval and a half-open one, so a partition such as $\left\{[0,1), [1,2), [2,3), [3,4]\right\}$ would have four parts of the same length/measure.