A half-life is the time taken for the radioactivity of a
material to fall to half its original value. A material can undergo
infinite half-lives because each time it falls to half the next
half-life falls to half of that half:
No half-lives have elapsed when radioactivity is at the original
amount; 1/1.
1 half-life is when radioactivity is at 1/2
2 half-lives is when radioactivity is at 1/4.
3 half-lives is when radioactivity is at 1/8.
4 half-lives is when radioactivity is at 1/16.
And so on.