Himpunan bilangan asli adalah {1, 2, 3, …}
Himpunan bilangan bulat adalah {…, -3, -2, -1, 0, 1, 2, 3, …}
Sepintas terlihat bahwa banyaknya bilangan bulat adalah sekitar dua kali lipat banyaknya bilangan asli.
Tapi sesungguhnya banyaknya bilangan asli sama dengan banyaknya bilangan bulat.
Alkisah terdapat dua kelas berisi siswa. Kelas A dan Kelas B.
Banyaknya siswa di kelas A akan sama dengan banyaknya siswa di kelas B, jika setiap siswa di kelas A memiliki tepat satu dan hanya satu pasangan siswa yang ada di kelas B.
Begitu pula dengan himpunan bilangan asli dan bilangan bulat, jika kita dapat memasangkan setiap bilangan asli dengan tepat satu bilangan bulat, maka niscaya banyaknya bilangan asli akan sama dengan banyaknya bilangan bulat.
Coba pasangkan
1 dengan 0
2 dengan 1
3 dengan -1
4 dengan 2
5 dengan -2
6 dengan 3
7 dengan -3
8 dengan 4
9 dengan -4
…
dan seterusnya.
Cocok kan?
Berarti semua bilangan asli akan selalu memiliki tepat satu pasangan bilangan bulat kan?
Artinya jika lawan Anda memilih suatu bilangan bulat, Anda selalu akan memiliki bilangan asli sebagai pasangannya, begitu pula sebaliknya. Misal, jika lawan Anda menantang dengan bilangan 77, maka Anda pasti dengan entengnya membalas dengan -38, begitu pula jika lawan Anda menantang dengan bilangan 1022, dan dengan tenang Anda akan menjawab 511. Dan seterusnya.
Kesimpulannya banyaknya bilangan asli sama dengan banyaknya bilangan bulat.
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