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Mathematics

Cardinal Arithmetic with Transfinite Numbers Beyond the Continuum

Quick fact

For any infinite cardinal κ, the sum and product with any smaller or equal cardinal μ simply equal κ: κ + μ = κ · μ = max(κ, μ). This means that the continuum 𝔠 added to itself is still 𝔠, and 𝔠 multiplied by itself is still 𝔠.

Why this is interesting

You've heard that some infinities are bigger than others, but did you know that when you add two infinite numbers together, the sum is exactly the same size? So what does it mean to multiply or raise them to powers?