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This primer exists for the background necessary to read our post on RSA encryption, but it also serves as a general primer to number theory. Oh, Numbers, Numbers, Numbers We start with some easy definitions. Definition: The set of integers, denoted $ \mathbb{Z}$, is the set $ \left \{ \dots -2, -1, 0, 1, 2, \dots \right \}$. Definition: Let $ a,b$ be integers, then $ a$ divides $ b$, denoted $ a \mid b$, if there exists an integer $ n$ such..
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This post assumes working knowledge of elementary number theory. Luckily for the non-mathematicians, we cover all required knowledge and notation in our number theory primer. So Three Thousand Years of Number Theory Wasn’t Pointless It’s often tough to come up with concrete applications of pure mathematics. In fact, before computers came along mathematics was used mostly for navigation, astronomy, and war. In the real world it almost always..
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This post assumes working knowledge of elementary number theory. Luckily for the non-mathematicians, we cover all required knowledge and notation in our number theory primer. So Three Thousand Years of Number Theory Wasn’t Pointless It’s often tough to come up with concrete applications of pure mathematics. In fact, before computers came along mathematics was used mostly for navigation, astronomy, and war. In the real world it almost always..
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This post assumes working knowledge of elementary number theory. Luckily for the non-mathematicians, we cover all required knowledge and notation in our number theory primer. So Three Thousand Years of Number Theory Wasn’t Pointless It’s often tough to come up with concrete applications of pure mathematics. In fact, before computers came along mathematics was used mostly for navigation, astronomy, and war. In the real world it almost always..
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The venerable O’Reilly Velocity Conference is coming to Berlin on the 8th and 9th of November. SoundCloud is doing what we can to help…
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The venerable O’Reilly Velocity Conference is coming to Berlin on the 8th and 9th of November. SoundCloud is doing what we can to help…
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Thanks to Jon at ISO50 (Scott Hansen’s beautiful Web site/blog) for mentioning / highlighting my Antarctic photography !
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Thanks to Jon at ISO50 (Scott Hansen’s beautiful Web site/blog) for mentioning / highlighting my Antarctic photography !
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Thanks to Jon at ISO50 (Scott Hansen’s beautiful Web site/blog) for mentioning / highlighting my Antarctic photography !
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When I was a kid, our family used to travel a lot. I grew up in central Europe and over the years, we visited most of continental Europe. This was in the early ’90s. Usually, Mom would have a map on her lap and she would tell Dad where to go. To keep me and my little brother entertained, they gave us another map and we would follow along. We had fun trying to pronounce funny city names and calculating distances that we had travelled that ..
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When I was a kid, our family used to travel a lot. I grew up in central Europe and over the years, we visited most of continental Europe. This was in the early ’90s. Usually, Mom would have a map on her lap and she would tell Dad where to go. To keep me and my little brother entertained, they gave us another map and we would follow along. We had fun trying to pronounce funny city names and calculating distances that we had travelled that ..
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False Proof—All Numbers are Describable in at Most Twenty Words
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www.jeremykun.com
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14 years ago
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eng
Problem: Show that every natural number can be unambiguously described in fewer than twenty words. “Solution”: Suppose to the contrary that not every natural number can be so described. Let $ S$ be the set of all natural numbers which are describable in fewer than twenty words. Consider $ R = \mathbb{N}-S$, the set of all words which cannot be described in fewer than twenty words. Since $ R$ is a subset of the natural numbers, which is well..
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False Proof—All Numbers are Describable in at Most Twenty Words
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www.jeremykun.com
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14 years ago
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eng
Problem: Show that every natural number can be unambiguously described in fewer than twenty words. “Solution”: Suppose to the contrary that not every natural number can be so described. Let $ S$ be the set of all natural numbers which are describable in fewer than twenty words. Consider $ R = \mathbb{N}-S$, the set of all words which cannot be described in fewer than twenty words. Since $ R$ is a subset of the natural numbers, which is well..
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False Proof—All Numbers are Describable in at Most Twenty Words
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www.jeremykun.com
-
14 years ago
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eng
Problem: Show that every natural number can be unambiguously described in fewer than twenty words. “Solution”: Suppose to the contrary that not every natural number can be so described. Let $ S$ be the set of all natural numbers which are describable in fewer than twenty words. Consider $ R = \mathbb{N}-S$, the set of all words which cannot be described in fewer than twenty words. Since $ R$ is a subset of the natural numbers, which is well..
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This post assumes familiarity with the terminology and notation of linear algebra, particularly inner product spaces. Fortunately, we have both a beginner’s primer on linear algebra and a follow-up primer on inner products. The Quest We are on a quest to write a program which recognizes images of faces. The general algorithm should be as follows. Get a bunch of sample images of people we want to recognize. Train our recognition algorithm on..
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This post assumes familiarity with the terminology and notation of linear algebra, particularly inner product spaces. Fortunately, we have both a beginner’s primer on linear algebra and a follow-up primer on inner products. The Quest We are on a quest to write a program which recognizes images of faces. The general algorithm should be as follows. Get a bunch of sample images of people we want to recognize. Train our recognition algorithm on..
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This post assumes familiarity with the terminology and notation of linear algebra, particularly inner product spaces. Fortunately, we have both a beginner’s primer on linear algebra and a follow-up primer on inner products. The Quest We are on a quest to write a program which recognizes images of faces. The general algorithm should be as follows. Get a bunch of sample images of people we want to recognize. Train our recognition algorithm on..
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Update 2023-10-17 The script has been verified to work in macOS Sonoma. When I switched from an older MacBook Pro to a MacBook Air the backup from my old MacBook Pro was corrupted and unmountable. However, I had preserved a backup of my Photo Booth Photos and wanted the Photo Booth application to recognize them. This is just a matter of creating a Recents.plist, an ordered list of the image files. While adding these photos to the Recent....
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Update 2023-10-17 The script has been verified to work in macOS Sonoma. When I switched from an older MacBook Pro to a MacBook Air the backup from my old MacBook Pro was corrupted and unmountable. However, I had preserved a backup of my Photo Booth Photos and wanted the Photo Booth application to recognize them. This is just a matter of creating a Recents.plist, an ordered list of the image files. While adding these photos to the Recent....
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To find the number of days until the end of the month, compare with the first day of the next month
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www.databasesandlife.com
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14 years ago
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eng
It’s a common enough problem, you want to find out if a date is in a particular month, or you want to know how many days there are left in the current month, and so on. I’ve seen the following awkward solution plenty of times at different companies: To find out if a day is within a month, you see if the date in question is greater than the start of the month and less than the end of the month; this seems logical enough. To determine the n..
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It is now possible to share all public tracks and playlists to the connections of the authenticated user. So if a user is already connected e.g. with Facebook on SoundCloud, this connection can be used from your app to share a track.
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It is now possible to share all public tracks and playlists to the connections of the authenticated user. So if a user is already connected e.g. with Facebook on SoundCloud, this connection can be used from your app to share a track.
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Hopefully getting pretty well polished by now. New features and fixes include: Twitter fix - spotted by piaqt and Matthieu Guyonnet-Duluc Tile and Breaking news service fix - spotted by fleon and McFly Long press on feeds for pin and remove on home screen, you may need to clear your current feeds for this to function correctly but didn’t want to force this in case it was unnecessary - suggested by Glenn and fleon Added News ma..
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Vector spaces alone are not enough to do a lot of the interesting things we’d like them to do. Since a vector space is a generalization of Euclidean space, it is natural for us to investigate more specific types of vector spaces which are more akin to Euclidean space. In particular, we want to include the notion of a dot product. By admitting additional structure to a vector space, we may perform more computations, and hopefully get more in..
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Vector spaces alone are not enough to do a lot of the interesting things we’d like them to do. Since a vector space is a generalization of Euclidean space, it is natural for us to investigate more specific types of vector spaces which are more akin to Euclidean space. In particular, we want to include the notion of a dot product. By admitting additional structure to a vector space, we may perform more computations, and hopefully get more in..
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Vector spaces alone are not enough to do a lot of the interesting things we’d like them to do. Since a vector space is a generalization of Euclidean space, it is natural for us to investigate more specific types of vector spaces which are more akin to Euclidean space. In particular, we want to include the notion of a dot product. By admitting additional structure to a vector space, we may perform more computations, and hopefully get more in..
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UPDATE: We made some changes to how we manage the App Gallery. Read about them here: The Next App Gallery Update So you’ve built a fantastic app that you would like to get showcased in the SoundCloud App Gallery? Here’s what you can do to improve your chances of getting your app featured and increase the likelihood of SoundCloud users trying out your app.
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UPDATE: We made some changes to how we manage the App Gallery. Read about them here: The Next App Gallery Update So you’ve built a fantastic app that you would like to get showcased in the SoundCloud App Gallery? Here’s what you can do to improve your chances of getting your app featured and increase the likelihood of SoundCloud users trying out your app.
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We present a video on Möbius transformations and the geometry of the sphere. Anyone who has taken or will take complex analysis (that means you engineers!) should watch this. It shows not only the beautiful correspondence between the two, but it reveals the intuition behind a lot of complex analysis, when more often than not a student is left in the dust of rigorous formulas. In short, this is a proof without words that the Möbius transform..
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We present a video on Möbius transformations and the geometry of the sphere. Anyone who has taken or will take complex analysis (that means you engineers!) should watch this. It shows not only the beautiful correspondence between the two, but it reveals the intuition behind a lot of complex analysis, when more often than not a student is left in the dust of rigorous formulas. In short, this is a proof without words that the Möbius transform..
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We present a video on Möbius transformations and the geometry of the sphere. Anyone who has taken or will take complex analysis (that means you engineers!) should watch this. It shows not only the beautiful correspondence between the two, but it reveals the intuition behind a lot of complex analysis, when more often than not a student is left in the dust of rigorous formulas. In short, this is a proof without words that the Möbius transform..
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I have a confession to make. I am not very consistent with upgrading my software. My iPhone 4 is about 6 months out of date and every time that the little updater came up in Snow Leopard on my MacBook Pro I just waved it off and told it to go away.
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Today we announce new activities available over the API. As a reminder: Activites are the items on your Dashboard.
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Today we announce new activities available over the API. As a reminder: Activites are the items on your Dashboard.
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Tonight’s the Night” A large volume of research goes into the psychological and behavioral analysis of criminals. In particular, serial criminals hold a special place in the imagination and nightmares of the general public (at least, American public). Those criminals with the opportunity to become serial criminals are logical, cool-tempered, methodical, and, of course, dangerous. They walk among us in crowded city streets, or drive slowly d..
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