More numbers between $2$ and $4$ than between $2$ and $3$? (I am not a mathematician.) Between $2$ and $3$ there are infinite numbers and between $2$ and $4$ there are infinite numbers.
So which "infinity" is greater?
 A: They are the same size infinity, specifically they both are the same size as the whole real line. To see that they are the same, notice we can map the interval $[2,3]$ onto the interval $[2,4]$ using the function $f(x)=2x-2$ this hits everything in $[2,4]$ since any $c$ in $[2,4]$ is hit by $(c+2)/2$which is in $[2,3]$ and only one thing hits $c$. (In this case we say that f is one-to-one and onto, which means f is a bijection. This is how we define"size" of infinite sets, if there exists a bijection between them, they are the same size.
A: Since you are not a mathematician, I will try to explain in simple terms why mathematicians consider that these two "infinities" are equal.
Imagine you have a classroom and you want to know whether you have more students than chairs (or the opposite). Then you ask the students to seat down and the result is clear: if some students are still standing, there are more students than chairs, if some chair is empty, there are more chairs than students. And if no student is standing and all chairs are occupied, there as as many chairs as students. Mathematically speaking, you have constructed a bijection between the set of students and the set of chairs: this just means that one associates with each student the chair on which he/she is sitting.
Now, when you have infinite sets, like the intervals [2, 3] and [2, 4] you are considering, mathematicians use the same idea to compare them: they try to establish a bijection between them. In this case, as explained in SE318's answer, the function $x \to 2x - 2$ gives a bijection between [2, 3] and [2, 4], that is, a correspondence that sends every element of [2, 3] to an element of [2, 4] such that (1) every element of [2, 4] is reached (see "all seats are occupied") and two distinct elements of [2, 3] are never sent to the same element of [2, 4] (see "a chair is occupied by only one student").
In this case, mathematicians say that the sets [2, 3] and [2, 4] have the same cardinality, which is a kind of measure to compare infinities.
By the way, Georg Cantor was probably the first mathematician to give a rigorous answer to your question.
