weird result trying to remove numbers from a list

[Exsul]

I'm trying to remove all the numbers from a list, but when I run the code, I get a strange result:

nums = [1, 2, 3, 4, 5]
words = ["I", "sing", "of", "arms", "and", "a", "man"]
both = nums + words

for each in both:
    if each in range(1000):
        both.remove(each)

print(both)

Output:
[2, 4, 'I', 'sing', 'of', 'arms', 'and', 'a', 'man']

Process finished with exit code 0

What are the 2 and 4 still there?