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We introduce translations in the rational plane. However we do not assume the conventional understanding of functions and mappings, which actually has some logical difficulties and conceptual disadvantages. We prefer a cleaner and more flexible understanding emphasizing the use of expressions. This video belongs to Wildberger's MathFoundations series, which sets out a coherent and logical framework for modern mathematics. Video Content: 00:00 Introduction 3:17 Approach to what a translation is 5:24 Example of how translation acts on a point 8:11 Composition ************************ Screenshot PDFs for my videos are available at the website http://wildegg.com. These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary. My research papers can be found at my Research Gate page, at https://www.researchgate.net/profile/... My blog is at http://njwildberger.com/, where I will discuss lots of foundational issues, along with other things. Online courses will be developed at openlearning.com. The first one, already underway is Algebraic Calculus One at https://www.openlearning.com/courses/... Please join us for an exciting new approach to one of mathematics' most important subjects! If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at / njwildberger Your support would be much appreciated. Here are the Insights into Mathematics Playlists: • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist Here are the Wild Egg Maths Playlists (some available only to Members!) • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist • Playlist ************************