Defining Half lives of radioactive isotopes

I had thought when the half life of an isotope was reached it would stop being radioactive. This is not the case. So, if an isotope like radioactive iodine that causes thyroid cancer has a half life of 8 days it means it takes 8 days for it to get from 1 full dose to 1/2 full dose of whatever radiation it was. Then 8 days later it will be 1/2 of the 1/2 or 1/4 of its orginal dose. Then 8 days later it will be 1/2 of 1/2 of 1/2 which would be 1/8 of the original dose.

So, when someone says Cesium or Caesium has a half life of 70 days that means in another 70 days after that it will be 1/2 of the previous 70 days in radiation strength and the same down to 1/4 of the original strength 70 days later etc.

Whereas when you are talking about Plutonium 239 at reactor number 3 it's half life is 25,000 years. But on a certain level all of us likely will be dead then when 25,000 years occurs. However, plutonium will still be at the same strength it is today until then and killing things all along the way wherever it blows to on the wind or water or land or vegetables or animals or humans and likely all of the above more than once during that time of 25,000 years, 50,000 years, 75,000 years and beyond.

One of the reasons plutonium is 2 million times more toxic to life on earth than uranium is because it is the "Gift that keeps on killing"-25,000 years, 50,000 years, 75,000 years and beyond.