The syntax is:

a[start:stop]  # items start through stop-1
a[start:]      # items start through the rest of the array
a[:stop]       # items from the beginning through stop-1
a[:]           # a copy of the whole array

There is also the step value, which can be used with any of the above:

a[start:stop:step] # start through not past stop, by step

The key point to remember is that the :stop value represents the first value that is not in the selected slice. So, the difference between stop and start is the number of elements selected (if step is 1, the default).

The other feature is that start or stop may be a negative number, which means it counts from the end of the array instead of the beginning. So:

a[-1]    # last item in the array
a[-2:]   # last two items in the array
a[:-2]   # everything except the last two items

Similarly, step may be a negative number:

a[::-1]    # all items in the array, reversed
a[1::-1]   # the first two items, reversed
a[:-3:-1]  # the last two items, reversed
a[-3::-1]  # everything except the last two items, reversed

Python is kind to the programmer if there are fewer items than you ask for. For example, if you ask for a[:-2] and a only contains one element, you get an empty list instead of an error. Sometimes you would prefer the error, so you have to be aware that this may happen.

Relationship with the slice object

A slice object can represent a slicing operation, i.e.:

a[start:stop:step]

is equivalent to:

a[slice(start, stop, step)]

Slice objects also behave slightly differently depending on the number of arguments, similar to range(), i.e. both slice(stop) and slice(start, stop[, step]) are supported. To skip specifying a given argument, one might use None, so that e.g. a[start:] is equivalent to a[slice(start, None)] or a[::-1] is equivalent to a[slice(None, None, -1)].

While the :-based notation is very helpful for simple slicing, the explicit use of slice() objects simplifies the programmatic generation of slicing.

The documentation implies this has a few useful properties:

word[:2]    # The first two characters
word[2:]    # Everything except the first two characters

Here’s a useful invariant of slice operations: s[:i] + s[i:] equals s.

For non-negative indices, the length of a slice is the difference of the indices, if both are within bounds. For example, the length of word[1:3] is 2.

I think we can assume that the range functions act the same for consistency.

They both behave exactly the same.

For some reason you expect the list's indexes to start from 0 and
the string's indexes to start from 1.

The fact is that they both start at 0.

As @Mark suggested in the comments, strings and lists indexing from Python's documentation.

You can use None:

arr=[0,1,2,3,4,5]
for i in range(0,3):
    print arr[:-i or None]

The ending indices (the 3's in 0:3 and 1:3) are exclusive, not inclusive, while the starting indices (0 and 1) are in fact inclusive. If the ending indices were inclusive, then the output would be as you expect. But because they're exclusive, you're actually only grabbing rows 0, 1, and 2, and columns 1 and 2. The output is the intersection of those, which is equivalent to the output you're seeing.

If you are trying to get the data you expect, you can do myNumpyArray[:, 1:]. The : simply grabs all the elements of the array (in your case, in the first dimension of the array), and the 1: grabs all the content of the array starting at index 1, ignoring the data in the 0th place.