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), it becomes . Students often struggle with this concept because it feels like it should be an infinitely small distance away from , but mathematically, there is no room between the two. We can prove this simply using basic fraction arithmetic: We know that If we multiply both sides by 33three-thirds is equal to , then must equal .

When a patient is dehydrated, in shock, or unable to take fluids by mouth, healthcare professionals reach for a bag of intravenous fluid. This solution contains exactly grams of salt per 0.9,en

opens the door to one of the most famous and mind-bending paradoxes taught in introductory calculus and real analysis. If you take a single , it is strictly less than . However, if you repeat that nine infinitely ( ), it becomes