A fragment of infinity happens when we count "one, two, three, four," or any sequential series of numbers, and conclude it by saying "and so forth, unto infinity." Note, this not infinity, it is only a fragment of it, which represents it.
We symbolize this repeated iteration with an ellipses, three dots which mean "and so forth, infinitely." This is how "1,2,3,4..." is a fragment of infinity to represent infinity.
We say that it represents an infinite sequence, meaning the full, complete infinity.
However, an infinity of fragments of infinity are still not enough to make one complete infinity. No one has ever completed a mathematical infinity, and no one ever will. It is simply impossible, the closest we'll ever get is a fragment.
Just like any number times zero is zero, infinity absorbs all: there is no way to combine even vastly huge fragments to equal a complete infinity. You will always need something more than a collection of infinity fragments to achieve a complete infinity.
Even an infinite number of such fragments, combined, does not equal infinity.