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Created: 2025-09-28
Type: Zettel
aliases:
References:
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tags:
- MATH31AH
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- All of calculus, and a lesser extent of linear algebra is about real numbers.
- We write real numbers in base 10, but this is a bit unnatural
> Definition: the set of real numbers is the set of infinite decimals, preceded by a plus or minus sign
- A number ending in all 9's is equal to a number ending in all 0's
- ex. $0.34999\dots=0.35000\dots$
- Also, $+.000\dots=-.000\dots$
- For $k\geq_{0}$, we will denote $[x]_{k}$ as the number with all of the digits of $x$ to the left of the decimal, and exactly $k$ digits after.
- Given two identical decimal constructions, $[x]_{k}$ will be the one with zeros.
- Given any two different numbers $x$ and $y$, one is always bigger than the other
