rational and irrational numbers

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is 0.1010010010001........ a rational or irrational number?

#Physics #General Physics

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Manish Shankar ·2009-07-17 22:36:36

I think its irrational

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341

Hari Shankar ·2009-07-17 23:14:48

check if the sequence of digits after the decimal is non-terminating and non-periodic.

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Celestine preetham ·2009-07-17 23:30:57

irrational

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Samarth Kashyap ·2009-07-17 23:39:30

This is a problem frm I.A.Maron's book

0.1010010001......1000...(n times)1.... is irrational
To prove this, it is necessary to ascertain that the gicven decimal fraction is not a periodic one. there are n zeroes between nth and (n+1)th unities, whcih cannot occur in a periodic function.

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Basic Integral Calculus Operators Symbols Matrix Cases

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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rational and irrational numbers

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