This issue of time being slices of zero length is better understood when put into one of the more familiar dimensions.
Do this and you'll come run into variations of
Zeno's Paradox which is well understood, and is based on the simple fallacy surrounding the mathematical equation:

So, try slicing up a 2x4. This little equation can be misused to say that you can create an infinite number of slices with width zero, and the sum of an infinite number of zero's is of course, zero. Therefore you can argue that your 2x4 has a length of zero even if it started out at 36. But the mathematical quantity "epsilon" (defined as "a number as small as you'd like it to be as long as its not zero" in colloquial terms), is still going to define a positive, non-zero width, if you're slicing, because its not possible to have an "infinite number of slices." So, no matter what, epsilon does have a width: You can slice a 2x4 as thin as you want, but the slices still have width. Therefore the logical conclusion is you can never create a short enough "now" for you to justify "there is no time."
This ought to be obvious, but with all things "time" and "infinite," people start getting very mystical.
Infinitely thin,
Buffy