A function f:X\longrightarrow Y is said to be 11 (read one-to-one) when f(x)\neq f(x') for all x,x'\in X with x\neq x'. A 11 function is also called an injection or we say that f is injective.
The Pigeon Hole Principle
A function \(f:X\longrightarrow Y\) is said to be \(1\)\(1\) (read one-to-one) when \(f(x)\neq f(x')\) for all \(x,x'\in X\) with \(x\neq x'\). A \(1\)\(1\) function is also called an injection or we say that \(f\) is injective. When \(f:X\longrightarrow Y\) is \(1\)\(1\), we note that \(|X|\le |Y|\). Conversely, we have the following self-evident statement, which is popularly called the Pigeon Hole principle.
In more casual language, if you must put \(n+1\) pigeons into \(n\) holes, then you must put two pigeons into the same hole.
Here is a classic result, whose proof follows immediately from the .
In , we will explore some powerful generalizations of the . All these results have the flavor of the general assertion that total disarray is impossible.
Sekarang kau
Tiada kalkulator yang dapat menyelesaikan ini, tetapi bahagian-bahagian boleh dikira. Cuba salah satu di bawah, atau taipkan sendiri.
Jaga kerja awak sendiri.
Akaun percuma menambah nota pada setiap pengajaran, rekod apa yang anda selesaikan, masalah yang anda selesaikan di satu tempat, dan seorang guru yang anda boleh tanya tentang halaman ini. Matematik itu sendiri terbuka kepada semua orang, sama ada anda log masuk atau tidak.
Tekan simbol mana-mana untuk definisi penuh, gambar, dan apa makna setiap huruf dalamnya.
Apa makna setiap bahagian
Bayangkan.
Bernilai mengetahui
Contoh
Juga digunakan dalam penjelasan itu
Soalan yang orang tanya
Permutation or combination?
Ask whether order matters. A lock code is a permutation (order matters); a hand of cards is a combination (it does not).
What is a graph in this sense?
Dots (vertices) joined by lines (edges), not a plot. Road maps, social networks and molecules are graphs; questions like "is there a route" and "how few colours" are graph theory.