Müntz–Szász theorem
Okay kiddo, so imagine you have a bag of marbles. Say you have a certain number of red marbles and blue marbles. Now, let's say you want to divide the marbles into different groups, so that each group has the same total number of marbles.
The question is: is it always possible to divide the marbles in this way? Well, the Müntz-Szász theorem tells us that it is possible if and only if the ratio of the number of red marbles to the number of blue marbles is what we call an "algebraic irrational number."
Now, an "algebraic irrational number" is just a fancy way of saying that it is a number that cannot be written as a simple fraction, but can be the solution to an algebraic equation (which is just a math problem with letters and numbers).
So, to sum it up, the Müntz-Szász theorem tells us that we can divide a bag of marbles into groups with the same total number of marbles, as long as the ratio of red to blue marbles is a special kind of number called an "algebraic irrational number."
The question is: is it always possible to divide the marbles in this way? Well, the Müntz-Szász theorem tells us that it is possible if and only if the ratio of the number of red marbles to the number of blue marbles is what we call an "algebraic irrational number."
Now, an "algebraic irrational number" is just a fancy way of saying that it is a number that cannot be written as a simple fraction, but can be the solution to an algebraic equation (which is just a math problem with letters and numbers).
So, to sum it up, the Müntz-Szász theorem tells us that we can divide a bag of marbles into groups with the same total number of marbles, as long as the ratio of red to blue marbles is a special kind of number called an "algebraic irrational number."