> Apakah setiap operasi matematis yang melibatkan infinite hasilnya
jadi tak tentu, tergantung bagaimana pola di area finite-nya?
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Alexander:
Tidak semua jawaban tak tentu, ada yang jawabannya pasti juga.
Contohnya:
1. (infinite) + finite = infinite
2. (infinite) + (infinite) = inifinite
>
>
> Maksud saya, apakah area yang infinite ini diluar jangkauan
konsistensi operasi matematis?
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Alexander:
Benar, banyak paradox muncul karena konsep infinite ini contohnya :
http://en.wikipedia
1. Burali-Forti paradox: If the ordinal numbers formed a set, it
would be an ordinal number which is smaller than itself.
2. Galileo's paradox: Though most numbers are not squares, there are
no more numbers than squares. (See also Cantor, Diagonal Argument)
3.Hilbert's paradox of the Grand Hotel: If a hotel with infinitely
many rooms is full, it can still take in more guests.
4.Skolem's paradox: Countably infinite models of set theory contain
uncountably infinite sets.
5. Supertasks can result in paradoxes such as the Ross-Littlewood
paradox and Benardete's paradox.
Salam,
Alexander Agung
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