Proof is left as an exercise to the reader is a phrase that tells the reader that a proof (or proof sketch) of something should be obvious from what has been said previously. The absence of a proof can then be used to argue for the truth or falsehood of a statement based on the conversational implicature that such a step would normally be required to prove it. It is typically used when one participant in a conversation takes on a burden of proof they are not willing to accept. The expression is often used jokingly, especially in relation to riddles, puzzles and parlor games.
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Proof is left as an exercise to the reader
The proof is left as an exercise for the reader.
The proof is left as an exercise for the reader.
Exercise reduces the risk of heart disease and cancer, as well as improving agility and balance.
The proof is left as an exercise for the reader.
Proof is left as an exercise for the reader.
Proof is left as an exercise for the reader, or rather a challenge to find it yourself (or ask on StackOverflow).
Proof is left as an exercise to the reader. This phrase is often used in mathematics and computer science to indicate that a proof of some result is not given, but that it can be obtained by the reader by applying methods from the rest of the text. It is also used in logic and philosophy to indicate that certain propositions are unprovable.
The phrase was first published in 1883 in The American Mathematical Monthly, where it was written by J. J. Sylvester as “the proof of this proposition is left as an exercise for the student”. The earliest recorded use of “proof is left as an exercise for the reader” outside mathematics was in 1929, when John Maynard Keynes wrote: “The proof of this proposition is left as an exercise for the reader.”
In addition to its use in mathematics and computer science, “proof is left as an exercise for the reader” has been used in several non-technical contexts:
In mathematics education research (see below).
To emphasize that something should be obvious or self-evident (e.g., “Proof is left as an exercise for you to do yourself”).
proof explained
As a joke (e.g., “Proof that unicorns exist is left as an exercise for
The proof is left as an exercise for the reader, which is a way of saying that the writer of a paper or book is not going to do the work for you. It’s up to you to think about what he or she has written and figure out what it means. The phrase can be used in many different ways.
For example, if you’re reading a math textbook, the author might say: “The proof is left as an exercise for the reader.” This means that they’ve done all the hard work and now they’re going to leave it up to you to figure out how they did it. Their job is done; now it’s your turn!
You could also use this phrase if someone asks you a question and then doesn’t answer it. For example:
Person A: What time does the movie start?
Person B: The proof is left as an exercise for the reader.*
Proof is left as an exercise to the reader is a sentence used to end a proof, or mathematical demonstration, to indicate that it is obvious that the proof is correct. It is often used in situations where the reader may have doubts about the validity of a proof and the author wishes to remove any such doubts.
The phrase was first used by Isaac Newton: “For though we cannot but conclude, upon just grounds, that God exists; yet our knowledge of his existence is not so great as if he had revealed himself unto us” (A Disquisition Upon The Prophecies).
The phrase has been used many times since then, including by Carl Friedrich Gauss in Disquisitiones Arithmeticae (1801) and by Hans Freudenthal in “On Constructing Surfaces with Given Boundary” (1948). The term was coined by physicist Richard Feynman in 1966 when describing how his approach to physics differed from others who were more interested in mathematics: “How do you know that’s true? I don’t think it’s true at all. But how do you know it isn’t so? How do you know there aren’t little green men on Mars?” He then went on to explain that he did not care whether this scenario was true or not
Exercise reduces the risk of developing high blood pressure, heart disease and diabetes. It also makes you feel better and lowers your risk of many other diseases. But how does exercise do all this?
The answer is that exercise increases the number of ‘good’ HDL cholesterol particles in your body. This helps to clear away bad LDL cholesterol particles from your blood vessels and arteries. Exercise also increases the size of your blood vessels so they can carry more oxygen-rich blood around your body (1, 2).
This article explains why exercise is so good for you, what happens when you don’t exercise and how much exercise you need to get these health benefits.
Evidence shows that physical activity can help reduce your risk of:
high blood pressure (hypertension) – by up to 50% (3)
heart disease – by up to 30% (4)
diabetes – by up to 50% (5)
cancer – especially breast cancer in women who are overweight or obese (6, 7)
Proof is left as an exercise for the reader.
The proof is left as an exercise to the reader meme can be a great way to remind people that they need to actually do the work and not just hand in their homework with no evidence that they did it. This meme can be used in any situation where you feel like someone else could use a little more effort.
This particular meme comes from a book called “The Art of Computer Programming,” which was written in 1968 by Donald Knuth. The first volume of this book is about fundamental algorithms, so it’s unlikely that anyone reading this would be able to solve all of the problems without some real work.
It’s hard to prove something that you don’t know. The proof is left as an exercise for the reader is a quote attributed to Euler, but there are no sources or citations for it. It might be real, but we don’t have any way of knowing.
This phrase has been used in mathematics books since at least the late 19th century. It was probably inspired by the fact that many mathematical proofs are fairly complicated and difficult to understand, so someone wanting others to understand the proof better would simply leave a gap where they were going to write down all their reasoning.
The phrase is used in two ways: when someone wants you to do some work for yourself and when someone doesn’t want you to know something because they want it to remain a mystery.
Here are some examples of this phrase being used:
The proof is left as an exercise for the reader. Theorem 1 follows from Theorem 2 by induction on n, or from Theorem 3 by applying Corollary 4 ….
Exercise reduces the risk of many health problems, including heart disease, stroke, and diabetes. It can also improve your mood and mental health.
Exercise can reduce your risk for health problems like heart disease and diabetes. It can also improve your mood and mental health.
Because exercise can have so many benefits for your health, it’s important to know how much you need to do to get these results. The recommendations below are based on age, sex and physical activity level:
If you’re a man who doesn’t exercise at all (including walking), start with 150 minutes of moderate-intensity aerobic physical activity or 75 minutes of vigorous-intensity aerobic physical activity every week (or a combination of these). If you have been inactive or haven’t exercised recently, start slowly with 10 minutes of light-intensity activity on most days of the week. As your fitness improves, gradually increase your activity until you are reaching the recommended amount each week.
If you’re a woman who doesn’t exercise at all (including walking), start with just 75 minutes of moderate-intensity aerobic physical activity or 150 minutes of vigorous-intensity aerobic physical activity every week (or a combination of these). If you have been inactive or haven’t exercised recently, start slowly with 10 minutes
Exercise reduces stress, improves mood, and increases energy. Exercise also helps with weight loss.
Exercise is any bodily activity that enhances or maintains physical fitness and overall health and wellness. It is performed for various reasons, including increasing growth and development, preventing aging, strengthening muscles and the cardiovascular system, honing athletic skills, weight loss or maintenance, and also for enjoyment. Frequent and regular physical exercise boosts the immune system, allowing the body to fight off infectious diseases more efficiently. Physical exercise has been shown to alleviate depression and anxiety, to improve self-esteem, to be a potential therapy for certain psychiatric conditions (such as dementia), to reduce overall mortality rates (see health benefits of physical activity) and to potentially decrease the risk of developing some forms of cancer.[citation needed] Many people choose to exercise publicly outdoors where they can congregate in groups such as runners’ clubs; while others prefer exercising indoors in places such as swimming pools or fitness centers.
In addition to health benefits,[1][2] physical exercise has been found to improve psychological outcomes in healthy adults.[3][4] In particular, aerobic exercise seems to produce positive effects on cognition.[5][6] For example