👉 Assumptions in mathematics refer to the implicit or explicit beliefs we hold about the world or properties of mathematical objects that guide our reasoning and problem-solving. These assumptions can range from basic axioms like the commutative property of addition to more complex ones about the nature of numbers or geometric shapes. For example, in Euclidean geometry, we often assume that parallel lines never intersect unless they are actually parallel, or that through a point not on a line, there is exactly one line parallel to the original line. These assumptions are crucial because they allow us to construct logical frameworks and derive theorems, but they can also be sources of debate and different mathematical systems (like non-Euclidean geometries) that arise when we challenge or modify these assumptions.
