By Amy Harris • Updated Aug 30, 2022
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In mathematics, infinity (∞) represents a quantity that grows without bound. It is not a finite real number, but rather a concept that describes limits that can become arbitrarily large.
Unlike ordinary numbers, operations involving infinity behave differently:
• ∞ + 1 = ∞ and ∞ + ∞ = ∞.
• Multiplying or dividing by a finite non‑zero number leaves the value at ∞.
Because it is unbounded, adding any finite quantity to infinity does not change its magnitude.
Students first encounter the idea of infinite sequences in middle‑school algebra, but the concept becomes essential in calculus when evaluating limits.
• The natural numbers 1, 2, 3, … form an infinite sequence.
• The decimal expansion of 2⁄3 is 0.666…; the digit “6” repeats ad infinitum.
• In geometry, a straight line extends indefinitely in both directions, unlike a line segment that has two fixed endpoints.
These examples illustrate how infinity appears across different areas of mathematics.
