BAB_5_INDUKSI_MATEMATIKA.pptx - BAB 5 Induksi Matematika 1 PENGERTIAN Metode pembuktian untuk pernyataan perihal bilangan bulat adalah induksi matematik

BAB_5_INDUKSI_MATEMATIKA.pptx - BAB 5 Induksi Matematika 1...

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BAB 5 Induksi Matematika 1
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Metode pembuktian untuk pernyataan perihal bilangan bulat adalah induksi matematik . Contoh : p ( n ): “Jumlah bilangan bulat positif dari 1 sampai n adalah n ( n + 1)/2” . Buktikan p ( n ) benar! 2 PENGERTIAN
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3 CONTOH
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Induksi matematik merupakan teknik pembuktian yang baku di dalam matematika. Melalui induksi matematik kita dapat mengurangi langkah-langkah pembuktian bahwa semua bilangan bulat termasuk ke dalam suatu himpunan kebenaran dengan hanya sejumlah langkah terbatas. 4
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Misalkan p(n) adalah pernyataan perihal bilangan bulat positif dan kita ingin membuktikan bahwa p(n) benar untuk semua bilangan bulat positif n. Untuk membuktikan pernyataan ini, kita hanya perlu menunjukkan bahwa: 1. p(1) benar, dan 2. jika p(n) benar maka p(n + 1) juga benar, untuk semua bilangan bulat positif n 1, 5 PRINSIP INDUKSI SEDERHANA.
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Langkah 1 dinamakan basis induksi , sedangkan langkah 2 dinamakan langkah induksi .
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