Why Does Math Break When You Add Infinity?

Imagine you have a magic basket that never fills up. If you put one apple in it every second, it gets bigger but is still empty enough to take more apples forever! This is infinity. But here is the surprise: not all infinities are equal size. The number of integers (1, 2, 3...) is infinite, and so is the number of decimals between zero and one. Yet, there are way more decimals than whole numbers. It feels wrong because we usually count things by matching them up. With infinity, you can match every whole number to a decimal, but some decimals will always be left out. This discovery changed how we understand space, time, and even computer code.