Category:Decimal Expansions

From ProofWiki
Jump to navigation Jump to search

This category contains results about Decimal Expansions.
Definitions specific to this category can be found in Definitions/Decimal Expansions.


Let $x \in \R$ be a real number.

The decimal expansion of $x$ is the expansion of $x$ in base $10$.


$x = \floor x + \ds \sum_{j \mathop \ge 1} \frac {d_j} {10^j}$:

$\sqbrk {s \cdotp d_1 d_2 d_3 \ldots}_{10}$

where:

$s = \floor x$, the floor of $x$
it is not the case that there exists $m \in \N$ such that $d_M = 9$ for all $M \ge m$.

(That is, the sequence of digits does not end with an infinite sequence of $9$s.)

Subcategories

This category has the following 6 subcategories, out of 6 total.

D

R

T