A mathematical object is an abstract concept arising in mathematics. Typically, a mathematical object can be a value that can be assigned to a symbol, and therefore can be involved in formulas. Commonly encountered mathematical objects include numbers, expressions, shapes, functions, and sets. Mathematical objects can be very complex; for example, theorems, proofs, and even formal theories are considered as mathematical objects in proof theory.
From left to right, top to bottom: A tesseract or four-dimensional hypercube, the graph of a binary function, a trefoil knot (a kind of mathematical knot), and a common hierarchy of sets of numbers.
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