I would like to share a paradox with you that could make eating your next hamburger very difficult. Imagine you are eating a delicious succulent hamburger, and in order to eat this burger you need to take bites from it. In taking a bite from it, you remove a portion, or a “fraction,” of the burger. Now, if we stop to think about how fractions work, it can be shown that it is impossible to finish eating your burger — from a mathematical perspective, that is.

Let’s say that you decide to eat your burger in fractions. If you take one massive bite — say you manage to eat half of it — then there is half of the original burger left. Now you decide to eat half of it again, leaving a quarter, and again, an eighth. If we follow this trend, you can see that you will continue getting smaller and smaller portions of burger, but that because you are always eating a half of the burger, you will always get a number greater than zero. So, that means that there will always be a bit of burger left to be eating, and therefore you cannot eat the entire burger.

Admittedly, the burger example isn’t really practical from a real world perspective, at one point you would just pop what’s left into your mouth, and be done with it. There is, however, a real world example that does follow the rule of being reduced by half: half-lives.

When talking about radiation, chemists talk in terms of half-lives, or the amount of time it takes for half of the atoms in a sample of radioactive material to decay. If you think about it, to go from 1 to one half takes X amount of time, for that half of the original sample to degrade by half also takes X amount of time, and so on and so forth. And, like in the burger analogy, you never really get down to zero, just smaller and smaller fractions of the original whole.

Speaking of zero, tune in next time for some fun with what some might call “the most interesting number.”