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  "body": "\n## Summary\n\nThe unitization of an algebra $A$ is the algebra $\\mathbb{K} \\oplus A$ with a product that makes $(1, 0)$ a unit.\nIt contains $A$ as an ideal of codimension one.\nIt lets one apply tools that need a unit, such as invertibility and the spectrum, to algebras without one.\nFor normed algebras and Banach algebras it carries a natural norm, and for C*-algebras a natural C*-norm.\n\n## Explanations\n\n### L1 human\n\nSome algebras have no element that acts like the number $1$, for example the continuous functions on $\\R$ that tend to $0$ at infinity.\nThe unitization adds such an element by hand.\nIts elements are formal sums $\\lambda + a$ of a scalar and an element of the algebra, multiplied by expanding the brackets.\nFor the functions vanishing at infinity, adding the constants gives the continuous functions on $\\R$ that have the same limit at $+\\infty$ and at $-\\infty$.\n",
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