ÇAĞDAŞ MATEMATİĞİN TEMELİ OLARAK KÜMELER KURAMI

19. yüzyıl matematiğinin önemli problemlerinden biri matematiğin temellendi- rilmesi meselesidir. Üretilen matematiksel bilginin doğruluğu ve kesinliği için matematiksel yapıların tek bir temele oturtulması ve bu sistemin kendi içinde tutarlı ve tam olması fikri dönemin matematik çevrelerinde geniş yankı bulmuş- tur. Birçok matematikçi temellendirme problemini çözme çalışmalarına önemli katkılarda bulunmuş, sonunda kümeler kuramı bir çözüm olarak doğmuştur. Kü- meler kuramı günümüzde kullanılan matematiksel yapıların büyük çoğunluğu için bir temel oluşturmanın yanında, kendi başına matematiğin önemli bir alanı olarak etkin varlığını sürdürür. Bu makalede kümeler kuramının doğuşunun 19. ve 20. yüzyıllarda izlediği tarihsel süreç incelenecek, ayrıca kümeler kuramının temel kavramları uzman olmayan okuyucu için açıklanacaktır.

SET THEORY AS FOUNDATION OF MATHEMATICS

Determining the foundations of mathematics has been one of the prominent problems of the 19th century mathematics. Mathematical society has found the idea of setting all mathematical objects on a unique, consistent and complete system as a brilliant one to decide truth and rigor of mathematical knowledge. Many mathematicians made significant contributions to the area, and at last, set theory emerged as a solution to the foundation problem. In additon to serve as a foundation to almost all mathematics we used today, set theory is a significant branch of mathematics in its own right. In this paper, the emerging of set theory in 19th and 20th centuries is examined and basic concepts of set theory is explained for non-mathematicians.

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