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Results tagged with examples
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user 4600
For questions requesting examples of a certain structure or phenomenon
2
votes
Examples of conjectures whose direct falsity implies different consequences than indirect fa...
Here's an example from computability theory.
Statement $A$:"The Turing degrees are linearly ordered".
Statement $B$: "The $\Sigma^0_1$ Turing degrees are linearly ordered".
Statement $A$ was refut …
- 24.8k
2
votes
58
votes
Is there a measure zero set which isn't meagre?
Let $p_i$ be a list of the rational numbers. Let $U_{i,n}$ be an open interval centered on $p_i$ of length $2^{-i}/n$. Then $V_n=\cup_i U_{i,n}$ is an open cover of the rationals, of measure at most $ …
- 24.8k
13
votes
Accepted
Example of a function that behaves like another function
This may be more than 15 symbols, but
$$
f(x)= x + \frac{1}{1+(x+\delta-1)^{2n/(2n-1)}}
$$
where $\delta>0$ is small and $n$ is large. For $n=2$ and $\delta=1/10$ it looks like this:
(source)
ED …
- 24.8k