ⵜⴰⵔ ⵡⵓⵜⵜⵓ ⵏ ⴽⴰⵏⵜⵓⵔ

**ⵜⴰⵔ ⵡⵓⵜⵜⵓ ⵏ ⴽⴰⵏⵜⵓⵔ** ⵜⴳⴰ ⵢⴰⵏ ⵓⵏⵥⴰ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴳ ⵜⵉⵥⵉⵕⵜ ⵏ ⵜⵔⵓⴱⴱⴰ ⵉⴼⵙⵔⵜ ⴰⵙⴳⴳⵯⴰⵙ 1891, ⵃⵎⴰ ⴰⴷ ⵉⵙⴱⴰⵢⵏ ⵉⵍⵉ ⵏ ⵜⵔⵓⴱⴱⴰ ⵏ ⵓⵟⵟⵓⵏⵏ ⵓⵔ ⵏⴳⴰⴱⴰⵍⵏ ⴷ ⵜⵔⵓⴱⴱⴰ ⵏ ⵓⵟⵟⵓⵏⵏ ⵉⴳⴰⵎⴰⵏⵏ ⵢⴰⴹⵏⵉⵏ.
## ⵜⴰⵣⵡⴰⵔⵜ
ⴷⴰⵜ ⵏ ⵜⴰⵙⵓⵜⴰ ⵡⵉⵙⵙ 19, ⵓⵔ ⵉⵍⵉ ⵢⴰⵏ ⵓⵔⴻⵎⵎⵓⵙ ⴱⴰⵀⵔⴰ ⵉⵅⴰⵜⴻⵔⵏ ⵅⴻⴼ ⵜⴰⵔ-ⵡⵓⵜⵜⵓ, ⵉⵎⵓⵙⵏⴰⴽⴻⵏ ⴳⴰⵏ-ⵜⵜⵉⵜ ⵣⵓⵏⴷ ⵢⴰⵜ ⵜⴰⵙⵎⴻⴽⵜⴰ ⴷ-ⵉⴽⴽⴰⵏ ⴰⴼⴻⵍⵍⴰ ⵏ ⵎⴰⵢⴷ ⴰⴽⴽⵯ ⵉⵍⵍⴰⵏ, ⵎⴰⵛ ⴰⵢⴷⴷⴻⵖ ⵔⴰⴷ ⵉⴱⴻⴷⴷⴻⵍ ⴰⴷ-ⴷⴰⵢ ⴷ-ⵉⵍⴰⵍ ⵓⵅⴰⵜⴰⵔ **ⵊⵓⵔⵊ ⴽⴰⵏⵜⵓⵔ** (ⵙ ⵜⴼⵕⴰⵏⵚⵉⵚⵜ'𝐆𝐄𝐎𝐑𝐆 𝐂𝐀𝐍𝐓𝐎𝐑) ⴳ 1845, ⴰⵔⵢⴰⵣ-ⴷⴷⴻⵖ, ⵙⵙⴻⴳ ⵜⴰⵎⵣⵢⵉⵜ-ⵏⵏⵙ ⴰⵢⴷ ⵖⵓⵔⵙ ⵜⴻḥⵍⴰ ⵜⵓⵙⵏⴰⴽⵜ ⴷ ⵎⴰⵢⴷ ⴰⵙ ⴰⴽⴽⵯ ⵉⴽⴽⴰⵏ ⵜⴰⵙⴳⴰ.. Aⵢⵏⵏⴰⵖ ⴰ ⵎⵉ, ⵍⵍⵉⵖ ⴳ ⵉⴳⴰ ⴰɛⴻⵔⵔⵉⵎ, ⵉⵙⵙⵓⴼⴻⵖⴷ ⵜⵉⵥⵔⵉ ⵏ ⵜⴳⵔⵓⵎⵎⵉⵡⵉⵏ ⵜⴰⵎⵣⵡⴰⵔⵓⵜ, ⴷⴰ-ⴰⵙ ⵜⵜⵉⵏⵉⵏ ⴷⵖⵉ ⵙ ⵜⴼⵔⴰⵏⵙⵉⵙⵜ “𝐥𝐚 𝐭𝐡𝐞𝐨𝐫𝐢𝐞 𝐧𝐚𝐢𝐯𝐞 𝐝𝐞𝐬 𝐞𝐧𝐬𝐞𝐦𝐛𝐥𝐞𝐬”, ⵙⵙⴻⴳ ⵜⵉⵥⵔⵉ-ⴷⴷⴻⵖ ⵉⵙⵙⵓⴼⴻⵖⴷ ⵢⴰⵏ ⵓⵔⴻⵎⵎⵓⵙ ⴰⵎⴻⵏⵖⵓⴷ ⵅⴻⴼ ⵜⴰⵔ-ⵡⵓⵜⵜⵓ, ⴷⴰⴷⴻⵖ ⴰⴳ ⵔⴰⴷ ⵢⴰⴼ 'Gⴻⵄⵔⴳ' ⴰⵢⴻⴷⴷⴰ ⵓⵔ ⵉⴷⵎⵉ, ⵢⵓⴼⴰⴷ ⵉⵙ ⵜⴰⵔ-ⵡⵓⵜⵜⵓ ⵜⴻⵍⵍⴰ ⴷⵉⴳⵙ ⵜⴰⵅⴰⵜⴰⵔⵜ, ⵜⴰⵎⵣⴰⵏⵜ, ⵜⴰⵏⴰⵎⴰⵙⵜ ⴷ ⵡⵓⴳⴳⴰⵔ.

ⴷⵖⵉ ⴰⴷⴷⵓ ⴰⵜ ⴰⵖⴷ ⴰⴷ ⵏⵣⵔⵉⵢ ⵙ ⵡⴰⵎⵎⴰⵙ, ⵉⴳ ⵏⴻⵏⵏⴰ **ⵜⴰⵔ-ⵡⵓⵜⵜⵓ** ⵍⵍⴰⵏⵜ ⴷⵉⴳⵙ ⵡⴰⵀⵍⵉ ⵏ ⵉⴷ ⵓⴷⴷⵓⴷ, ⵉⴱⴻⴷⴷⴰⴷ ⴰⴷ ⵜⵉⵍⵉ ⵢⴰⵜ ⵖⵉⴼⵙⴻⵏⵜ ⴰⴽⴽⵯ ⵉⵎⵥⵥⵉⵢⴻⵏ ??
Iⵡⴰ ⴼⵉɛⵍⴰⵏ ⵀⴰⵜ ⵏⵉⵜ ⵜⵍⵍⴰ, ⵜⴰⵔ ⵡⵓⵜⵜⵓ ⴷⴷⵖ ⴷⴰⵙ ⵜⵜⵉⵏⵉⵏ (𝐚𝐥𝐞𝐩𝐡 𝐧𝐮𝐥𝐥)ⴰⵔ ⵜ-ⵏⵜⵜⵓⵔⵓ ⵙ ℵ₀, ⵏⵜⵜⴰⵜ ⴰⵢⴷ ⵉⴳⴰⵏ ⵓⴷⴷⵓⴷ ⵏ ⵜⴰⴳⵔⵓⵎⵎⴰ ⵏ ⵓⵎⵎⵉⴷⴻⵏ ⵉⴳⵎⴰⵡⵉⵜⴻⵏ ℕ = {0, 1, 2, …}, ⴷ ⵓⵔ-ⵉⴷⴷ ⵖⴰⵔ ⵡⴰⴷⵖ ⴰⵢⴷ ⵉⵍⵍⴰⵏ... ⴰⵡⴷ ℤ = {…, -2, -1, 0, 1, 2, …} ⵉⵍⴰ ⵖⵓⵔⵙ ⴰⵎⵎ ⵡⵓⴷⴷⵓⴷ ⵏ ℕ, ⵉⵍⵍⴰ ⴷⵉⴳⵓⵏ ⵡⵉⵏⵏⴰ ⵔⴰⴷ ⵢⵉⵏⵉⵏ ⴷⵖⵉ, ⵎⴰⵜⴰ ⵜⵉⵎⵎⵉⵄⴹⵕⵟ-ⵉ ?? Aⵛⴽⵓ ⴷⴰ-ⵏⴻⵜⵜⵉⵖⵉⵍ ⵉⵙ ⵢⵓⴳⵔ ℤ - ℕ ⵎⴰⵛ ⵀⴰⵜ ⵢⴰⵏ ⵡⵓⴷⴷⵓⴷ ⴰⵢⴷ ⵖⵓⵔⵙⵏⵜ ⴰⴽⴽⵯ, ⴷ ⴰⴼⴰⴷ ⴰⴷ ⴰⵡⴻⵏⵜ ⵏⵎⴻⵍ ⵉⴱⴷⴷⴰⴷ ⴰⴷ ⵏⵓⵖⵓⵍ ⵙ-ⵓⵔⵎⵎⵓⵙ ⵏ ⵜⵙⵖⵏⵉⵏ ⵜⴰⵙⵏⴳⵉⵔⵉⵏ.
## ⵜⵉⵎⵥⵕⵉ ⵏ ⴽⴰⵏⵜⵓⵔ
ⴰⵔⵎⵎⵓⵙ-ⴷⴷⵖ ⵉⴱⴷⴷⴰ ⵅⴼ ⵓⵙⵎⴰⵜⴰ ⵏ ⵓⵣⴷⴰⵢ ⴷⴷⴰ ⵏⵙⴽⴰⵔ ⴽⵓ ⴰⵙⵙ ⵎⴰⵛ ⵓⵔ ⴷⴰ ⴰⵙ ⴷ-ⵏⵜⵜⴰⵡⵉ ⵉⵏⵖⵎⵉⵙⵏ, ⴰⵎⵎ ⵉⴳ-ⵔⵉⵖ ⴰⴷ ⵉⵏⵉⵖ ⵀⴰⵜ 5 ⵏ ⵉⴹⵓⴹⴰⵏ ⴰⵢⴻⴷ ⵉⵍⵍⴰⵏ ⴳ ⵓⴼⵓⵙ ⴰⵥⴻⵍⵎⴰⵟ ⵓⵍⴰ ⴰⵢⴻⴼⴼⴰⵙ, ⵖⵉⵖ ⴰⴷ-ⴷⴰⵢ ⵙⵎⵓⵏⴻⵖ ⵉⴼⴰⵙⵙⴻⵏ, ⵙⴻⵔⵙⴻⵖ ⴰⵜⴰⴹ ⵅⴼ ⵓⵟⴰⴹ ⵀⴰⵏ ⵜⴰⵙⵖⵯⵏⵜ ⵜⴰⵙⵏⴳⵉⵔⵜ ⵏⴳⵔ ⵓⵟⴰⴹ ⴰⵢⴻⴼⴼⴰⵙ ⴷ ⵓⵥⴻⵍⵎⴰⵟ, ⴰⵛⴽⵓ ⴽⵓ ⵓⵟⴰⴹ ⵉⵎⴰⵏ ⴷ ⵢⵉⵡⴻⵏ ⵓⵟⴰⴹ ⴳ ⵓⴼⵓⵙ ⴷⴷⴰⵖ ⴰⵟⵏⵉⵏ ⴷ ⵓⵔ ⵏⵜⵜⵓ ⴰⵡⴷⵢⴰⵏ. 
Iⵡⴰ ⵀⴰⵜ ⴰⵎⵎ ⵉⵎⴽⵉ ⴰⵢⴷ ⵏⵙⵙⴽⴰⵔ ⴳ ⵜⵓⵙⵏⴰⴽⵜ, ⵉⴳ ⵖⵓⵔⵏⵏⵖ ⵍⵍⴰⵏⵜ ⵙⵏⴰⵜⵜ ⵜⵉⴳⵔⵓⵎⵎⴰ 𝐗 ⴷ 𝐘, ⴷⴰ ⵏⴻⵜⵜⵉⵏⵉ 𝐗 ⴷ 𝐘 ⵉⵍⵍⴰ ⵖⵓⵔⵙⴻⵏⵜ ⵢⴰⵏ ⵡⵓⴷⴷⵓⴷ ⵉⴳ ⵏⵖⵉ ⴰⴷ ⵏⴰⴼ ⵢⴰⵜ ⵜⴰⵙⴻⵖⵯⵏⵜ ⵜⴰⵙⴻⵏⴳⵉⵔⵜ ⵙⵙⴻⴳ 𝐗 ⵙ 𝐘, ⵏⴻⵥⴹⴰⵔ ⴰⴷ ⵏⴻⵣⴷⵉ ⴽⵓⵍⵍⵓ ⵉⴼⵔⴷⵉⵙⴻⵏ ⵏ 𝐗 ⵙ ⵡⵉⵏ 𝐘 ⴱⵍⴰ ⵏⴻⵜⵜⵓ ⵡⵍⴰ ⵏɛⴰⵡⴻⴷ ⴰⵡⴷⵢⴰⵏ ⵓⴼⵔⴷⵉⵙ.
‎
Iⴳ ⵏⴰⵖⵓⵍ ⵙ ⵓⵎⴷⵢⴰ ⵏ ℕ ⴷ ℤ, ⵏⴻⵥⴹⴰṛ ⴰⴷ ⵏⴰⴼ ⵢⴰⵜ ⵜⴰⵙⵖⵯⵏⵜ ⵜⴰⵙⴻⵏⴳⵉⵔⵜ ⴳⵔ-ⴰⵙⵏ, ⵉⴳ ⵖⵓⵔⵏⵏⴻⵖ ⵉⵍⵍⴰ ⵢⴰⵏ ⵓⵎⵎⵉⴷ ⴰⴳⵎⴰⵡⵉⵢ 𝑛∈ℕ, ⴰⴷ ⵏⵙⴻⵔⵙ 𝑓(𝑛) = 𝑛/2 ⵉⴳ ⵉⴳⴰ 𝑛 ⴰⵢⵓⴳⴰⵏ, ⵏⵙⴻⵔⵙ 𝑓(𝑛) = -(𝑛+1)/2 ⵉⴳ ⵓⵀⵓ, ⵉⵎⴽⵉⴷⴷⵖ ⵀⴰⵜ ⵏⵀⵀⵢⵢⴰ 𝑓 ⴷ ⵜⴳⴰ ⵜⴰⵙⵖⵯⵏⵜ ⵜⴰⵙⵏⴳⵉⵔⵜ, ⵉⵡⴰ ⴷⵖⵉ ⵏⴻⵥⴹⴰⵕ ⴰⴷ ⵏⵉⵏⵉ ℕ ⴷ ℤ ⵉⵍⵍⴰ ⵖⵓⵔⵙⵏ ⵢⴰⵏ ⵡⵓⴷⴷⵓⴷ.
Nⴻⵥⴹⴰṛ ⴰⴷ ⵏⴷⴷⵓ ⵓⴳⴳⴰⵔ ⵏ ⵓⵢⴰ, ⴰⵡⴷ ⵜⴰⴳⵔⵓⵎⵎⴰ ⵏ ⵓⵎⵎⵉⴷⵏ ⵉⵎⵖⵥⴰⵏⵏ ℚ = {0, 1, ½, -1/3, 5, -11/20...}, ⵡⵍⴰ ⴰⵡⴷ ⵜⴰⴳⵔⵓⵎⵎⴰ ⵏ ⵉⵎⵏⵣⴰ 𝐏 = {2, 3, 5, 7, 11, ...}, ⵉⵍⵍⴰ ⵖⵓⵔⵙⵏⵜ ⵢⴰⵏ ⵡⵓⴷⴷⵓⴷ ⵉⴳⴰⵏ ℵ₀.
‎
ⵟⴰⵕⵟ ⴰⵍⵃⵀ ⵏⵓⵍⵍ, ⵎⴰⵜⵜⴰ ⵡⵓⴷⴷⵓⴷ ⵏ ⵜⴰⵔ-ⵡⵓⵜⵜⵓ ⴷ-ⵉⴽⴽⴰⵏ ⵟⴰⵔⴰⵙ ? 
Dⴰⴷⴻⵖ ⴷⴰ ⴷ-ⵉⵜⵜⴷⴷⵓ ⵓⵅⴰⵜⴰⵔ ⵏⵏⴻⵖ ℝ ⵉⴳⴰⵏ ⵜⴰⴳⵔⵓⵎⵎⴰ ⵏ ⵓⵎⵎⵉⴷⴻⵏ ⵉⵍⴰⵡⴻⵏ, ⵓⴷⴷⵓⴷ-ⵏⴻⵙⵙ ⴷⴰⵙ ⵜⵉⵏⵉⵏ ⴰⵍⴻⵃⵀ-ⵄⵏⴻ ⴰⵔ ⵜ-ⵜⵜⵓⵔⵓⵏ ⵙ ℵ₁.
'Cⴰⵏⵜⵄⵔ' ⵉⴼⴻⵔⵔⴻⵣ ⵉⵙ ⵢⵓⴳⴻⵔ ℵ₁, ℵ₀, ⵉⴼⴻⵔⵔⴻⵣⵜ ⵙ-ⵡⴰⵏⵥⴰ ⵓⴱⴷⵉⵙ, ⵀⴰⵏ ⴰⵙⵖⵓⵏ-ⵏⵏⵙ ⵉ ⵡⴰⵏⵏⴰ ⵉⵔⴰⵏ ⴰⴷ ⵖⵉⴼⵙ ⵢⵉⵙⵉⵏ ⵓⴳⴳⴰⵔ.
‎
Iⵎⴽⵉⴷⴷⴰⵖ ⴰⵖ ⵉⵊⵔⴰⵏ ⴳ ⵓⵎⴷⵢⴰ ⵏ ℕ ⴷ ℤ ⵎⵓ ⵖⵓⵔ ⵉⵍⵍⴰ ⵢⴰⵏ ⵡⵓⴷⴷⵓⴷ, ⴳ ℝ ⵉⵍⵍⴰ ⵎⴰⵢⴻⴷ ⵉṣṣⴻṛɛⴰⴱⴻⵏ ⵓⴳⴳⴰⵔ, ⵏⴻⵥⴹⴰṛ ⴰⴷ ⵏⴼⴻⵔⵔⴻⵣ ⵉⵙ ⵎⴰⵢⴻⴷ ⴰⴽⴽⵯ ⵉⴳⴰⵏ ⴰⵣⵉⵍⴰⵍ ]𝑎,𝑏[ ⵀⴰⵜ ⵓⴷⴷⵓⴷ-ⵏⴻⵙⵙ ⵉⴳⴰ ⴰⵎⵎ ⵡⵉⵏ ℝ ⴰⵢⴻⵏⵏⴰ ⵙ-ⵔⴰⵏ ⴳⵉⵏⵜ 𝑎,𝑏∈ℝ (ⴰ<ⴱ); ⵜⴰⵙⵖⵯⵏⵜ ⵜⴰⵙⴻⵏⴳⵉⵔⵜ ⵉⵍⵍⴰⵏ ⴳⴻⵔ ]𝑎,𝑏[ ⴷ ℝ ⵜⴳⴰ-ⵜⵜⵉⵜ 𝑓(𝑥) = 1/(𝑥-𝑎) + 1/(𝑥-𝑏).
Hⴰⵜ ⴰⵡⴷ ℂⁿ ⴷ ℝⁿ ⵢⴰⵏ ⵡⵓⴷⴷⵓⴷ ⴰⵢⴷ ⵖⵓⵔⵙⴻⵏ ⴰⴽⴽⵯ ⵉⵍⵍⴰⵏ ⵏⵉⵜⵏⵉ ⵓⵍⴰ ℝ, ⴰⵢⴻⵏⵏⴰ ⵙ ⵉⵔⴰ ⵉⴳⴻⵜ ⵏ∈ℕ*.
‎
ⵏⵥⴹⴰⵕ ⴰⴷ ⵏⴷⴷⵓ ⵓⴳⴳⴰⵔ ⵏ ℵ₁, ⵜⴰⵖⴰⵔⴰⵙⵜ ⴰⴼⴰⴷ ⴰⴷ ⵏⴳⵓⵍⵓ ℵ₂, ⵜⴳⴰ-ⵜⵜⵉⵜ ⴰⴷ ⵏⴰⵙⵉ ⵜⴰⴳⵔⵓⵎⵎⴰ ⵏ ⵉⵎⵓⵔⴻⵏ 𝒫(ℝ) ⵏ ℝ, ⵟⴰṛⵟ ℵ₂, ⵏⴻⵥⴹⴰṛ ⴰⴷ ⵏⴰⵙⵉ ⵜⴰⴳⵔⵓⵎⵎⴰ ⵏ ⵉⵎⵓⵔⴻⵏ ⵏ 𝒫(ℝ) ⵉⴳⴰⵏ 𝒫(𝒫(ℝ)), ⴰⵔ ⵜⴻⴷⴷⵓⵜ ⵉⵎⴽⵉⵏⵏⴰⵖ ⴰⵔ ⴷ-ⵜⴻⵡⴻḥⴻⵍⵜ..
‎
ⴳ ⵜⵉⴷⵜ ⵀⴰⵜ ⵉⵍⵍⴰ ⵓⵜⵜⵓ ⵏ ⵡⵓⵢⴷⴷⵖ ⴰⴽⴽⵯ, ⵜⴳⴰ-ⵜⵜⵉⵜ **ⵜⴰⵔ ⵡⵓⵜⵜⵓ ⵜⴰⵎⴰⴳⴷⵣⵜ** ⴷⴰ ⴰⵙ ⵜⵜⵉⵏⵉⵏ *OMEGA* ⴰⵔ ⵜ-ⵜⵜⵓⵔⵓⵏ ⵙ Ω, ⵜⴳⴰ ⴰⵎⵎ ⵢⴰⵜ ⵜⵖⴰⵙⵡⴰ ⵓⵙⴰⵔ-ⵏⵏ-ⵏⴳⵓⵍⴰ, ⵎⵇⵇⴰⵔ ⵜⵏⵏⵉⵜ-ⵏⵍⵎⴰⵍⴰ ⴰⵔⴷ ⵏⵕⵎⵉ, ⵜⵓⴳⵔ ⵎⴰⵜⵜⴰ ⵜⴰⵙⵎⴻⴽⵜⴰ ⵉⵍⵍⴰⵏ ⵜⴳⵉⵜ ⵜⴰⵎⴼⵓⴽⴻⵜ ⵏⵖⴻⵔ ⵓⵔ ⵜⵜⵉⵜ-ⵜⴳⵉ.
'ⵛⴰⵏⵜⵄⵔ' ⵉⵥⵕⴰ ⴰⵢⴷⴷⵖ ⵏ Ω ⴰⵎ ⵜⴰⵡⵍⴰⴼⵜ ⵏ Ṛⴻⴱⴱⵉ ⴳ ⵜⵓⵙⵏⴰⴽⵜ ⴷ ⵉⵙ ⵜⴳⴰ ⵡⵓⵜⵜⵓ ⵏ ⵎⴰⵢⴻⴷ ⴰⴽⴽⵯ ⵉⵍⵍⴰⵏ ⴷ ⵎⴰⵢⴻⴷ ⵓⵔ ⵉⵍⵍⵉⵏ.

‎==ⵉⵙⴰⵖⵓⵍⵏ==