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- real analysis - Proving that the interval $ (0,1)$ is uncountable . . .
I'm trying to show that the interval $(0,1)$ is uncountable and I want to verify that my proof is correct My solution: Suppose by way of contradiction that $(0, 1)$ is countable Then we can crea
- Uncountable vs Countable Infinity - Mathematics Stack Exchange
My friend and I were discussing infinity and stuff about it and ran into some disagreements regarding countable and uncountable infinity As far as I understand, the list of all natural numbers is
- Why is $\ {0,1\}^ {\Bbb N}$ uncountable? [duplicate]
We know the interval $ [0, 1]$ is uncountable You can think of the binary expansions of all numbers in $ [0, 1]$ This will give you an uncountable collection of sequences
- Proving a set is uncountable - Mathematics Stack Exchange
A set $A$ is countable if $A\approx\mathbb {N}$, and uncountable if it is neither finite nor countably infinite
- real analysis - Show that $ (0, 1)$ is uncountable if and only if . . .
What's the definition of countable and uncountable This simply cries out to me that we must find a 1-1 correspondence between (0,1) and R
- set theory - What makes an uncountable set uncountable? - Mathematics . . .
And since $\aleph_0$ is the cardinality of any countable set, this means that this power set must be uncountable Some other ways to construct infinite sets are simply to add elements to an existing set by taking the union of an arbitrary set and known uncountable sets
- elementary set theory - What do finite, infinite, countable, not . . .
We can use the above theorem to show that $\mathbb R$ is in fact with bijection with $\mathcal P (\mathbb N)$, and therefore $\mathbb R$ is not countable Since the above shows that $\mathbb R$ is uncountable, and $\mathbb R\subseteq\mathbb C$ we have that the complex numbers are also uncountable
- Help understanding countable and uncountable infinities
just had some questions about countable and uncountable infinities If we take a limit that results in $\frac { \infty } {0}$, we typically conclude that the limit is just $\infty$, correct? But if
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