We consider the function f α,on the interval (0, ∞), where α = (a 1 , a 2 , . . . , a n ),, Hiai and Kosaki define the relation using positive definiteness for functions f and g with some suitable conditions and they have proved this relation implies the operator norm inequality associated with functions f and g. In this paper, we give some conditions for α ′ , β ′ ∈ R m to hold the relation f α,β (t) f α ′ ,β ′ (t).
Penelitian ini bertujuan untuk mendeskripsikan kesulitan siswa dalam menyelesaikan masalah matematika dengan induksi. Penelitian ini menggunakan jenis penelitian studi kasus dengan pendekatan kualitatif. Subjek penelitian ini adalah 2 siswi kelas XI SMA IPA. Subjek Pertama (Siswa A) merupakan siswi di salah satu SMA Negeri di Jakarta dan subjek kedua (Siswa B) merupakan siswi di salah satu Homeschooling di Jakarta. Instrumen penelitian yang digunakan adalah tes dan wawancara. Hasil penelitian menunjukkan bahwa siswa masih mengalami kesulitan dalam menyelesaikan pembuktian dengan induksi matematika, hal ini terlihat dari kesalahan yang dilakukan siswa dalam menyelesaikan permasalahan dengan induksi matematika. Kesalahan tersebut adalah kesalahan konsep dan kesalahan operasi aljabar. Kesalahan konsep yang dilakukan adalah siswa tidak memahami makna “n” dalam induksi matematika. Siswa terbiasa menyelesaikan soal induksi matematika yang dimulai dari basis induksi n = 1. Selanjutnya pada tahap P(k+1), kesalahan konsep yang dilakukan adalah siswa tidak memahami maksud “k+1”. Siswa melupakan tahap n = k saat menyelesaikan P(k+1) sehingga dalam menyelesaikan pembuktian tidak diperoleh hasil yang benar. Kesalahan operasi terjadi saat proses pembuktian dengan induksi. Pada tahap P(k+1), siswa mengalami kesulitan dalam pengoperasian bentuk aljabar. Kesalahan ini terjadi karena siswa belum memahami materi operasi bentuk aljabar dengan baik. This study aims to describe students' difficulties in solving mathematical problems by induction. This research uses a case study research type with a qualitative approach. The subjects of this study were 2 students of class XI SMA IPA. The first subject (Student A) is a student at a public high school in Jakarta and the second subject (Student B) is a student at a Homeschool in Jakarta. The research instruments used were tests and interviews. The results showed that students still had difficulties in completing the proof by mathematical induction, this could be seen from the mistakes made by students in solving problems with mathematical induction. These errors are conceptual errors and algebraic operations errors. The conceptual error made is that students do not understand the meaning of "n" in mathematical induction. Students are accustomed to solving mathematical induction problems starting from basic induction n = 1. Then at the P(k+1) stage, the conceptual error made is that students do not understand "k+1". Students forget the step n = k when completing P(k+1) so that in the completion they do not get the correct result. operating errors that occur during the inspection process by induction. At stage P(k+1), students have difficulty operating algebraic forms. This error occurs because students do not understand the material of algebraic operations well.
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