0,(9) sahifasining manbasini koʻrish

[[Tasvir:999 Perspective 2.svg|300px|right]]
'''0,(9)''' yoki '''0,999…''' („nol va davrda toʻqqiz“) [[matematika]]da [[oʻnli kasr|oʻnli]] [[davriy kasr]] boʻlib, [[1 (son)|1ga]] tengdir. Yaʼni „0,999…“ ham, „1“ ham aynan bir [[son]]dir<ref>This definition is equivalent to the definition of decimal numbers as the limits of their summed components, which, in the case of 0.999..., is the limit of the sequence (0.9, 0.99, 0.999, ...).  The equivalence is due to bounded increasing sequences having their limit always equal to their [[least upper bound]].</ref>.

Ushbu ayniyatni isbotlovchi bir necha [[matematik isbot]] mavjud.
Masalan:
: <math>\frac{1}{3} = 0{,}333\ldots = 0{,}(3);</math>
: <math>1 = 3 \cdot \frac{1}{3} = 0{,}999\ldots = 0{,}(9).</math>
yoki
<br />
<math>
\begin{align}
x        &= 0{,}(9); \\
10 x     &= 9{,}(9); \\
10 x - x &= 9{,}(9) - 0{,}(9); \\
9 x      &= 9{,}0; \\
x        &= 1. 
\end{align}
</math>

== Manbalar ==
{{manbalar}}

{{math-stub}}

[[Turkum:Matematika]]
[[Turkum:Matematik paradokslar]]