Suslin's problem: Difference between revisions

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{{Other uses}}
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In [[mathematics]] and [[computer science]], '''truncation''' is the term for limiting the number of [[numerical digit|digit]]s right of the [[decimal point]], by discarding the least significant ones.
 
For example, consider the [[real number]]s
 
:5.6341432543653654
:32.438191288
:−6.3444444444444
 
To ''truncate'' these numbers to 4 decimal digits, we only consider the 4 digits to the right of the decimal point.
 
The result would be:
 
:5.6341
:32.4381
:−6.3444
 
Note that in some cases, truncating would yield the same result as [[rounding]], but truncation does not round up or round down the digits; it merely cuts off at the specified digit. The truncation [[Approximation error|error]] can be twice the maximum error in rounding.
 
== Truncation and floor function ==
{{main|Floor and ceiling functions}}
Truncation of positive real numbers can be done using the [[floor function]]. Given a number <math>x \in \mathbb{R}_+</math> to be truncated and <math>n \in \mathbb{N}_0</math>, the number of elements to be kept behind the decimal point, the truncated value of x is
:<math>\operatorname{trunc}(x,n) = \frac{\lfloor 10^n \cdot x \rfloor}{10^n}.</math>
 
However, for negative numbers truncation does not round in the same direction as the floor function: truncation always rounds toward zero, the floor function rounds towards negative infinity.
 
== Causes of truncation ==
With computers, truncation can occur when a decimal number is [[type conversion|typecast]] as an [[integer]]; it is truncated to zero decimal digits because integers cannot store [[real numbers]] (that are not themselves integers).
 
== In algebra ==
An analogue of truncation can be applied to [[polynomial]]s. In this case, the truncation of a polynomial ''P'' to degree ''n'' can be defined as the sum of all terms of ''P'' of degree ''n'' or less. Polynomial truncations arise in the study of [[Taylor polynomial]]s, for example.<ref>{{cite book|first=Michael|last=Spivak|title=Calculus|edition=4th|year=2008|isbn=978-0-914098-91-1|page=434}}</ref>
 
== See also ==
* [[Arithmetic precision]]
* [[Floor function]]
* [[Quantization (signal processing)]]
* [[Precision (computer science)]]
* [[Truncation (statistics)]]
 
== References ==
{{Reflist}}
 
== External links ==
* [http://to-campos.planetaclix.pt/fractal/walle.html Wall paper applet] that visualizes errors due to finite precision
 
[[Category:Numerical analysis]]
 
[[ja:端数処理]]

Revision as of 19:46, 2 March 2014

We have a objective to lose weight swiftly and these rapidly fat reduction tips are written to aid you reach that goal. Losing fat quick can happen for you however I may inform we that in the event you are not willing to place forth the effort needed you'll not get the results you want. These tips can require the effort but when you have the desire to receive the weight off the body now, this article usually show we how.

Leafy greens are excellent inside fiber, low in calories, packed full of compounds, plus approximately half their digestible calories come from protein. Eating at least 10 servings of greens a day could replace a lot of the higher calorie foods in the diet, yet leave we just as full. If you should lose weight fast, eat the greens. If you have to lose weight faster, eat MORE greens. I highly suggest drinking a green smoothie for breakfast every morning.

This could be possible, yet many folks that resort to quick weight reduction programs moreover very immediately may usually gain it back. Because fast fat reduction is frequently accomplished by drastically reducing calories, reintroducing the same amount of food signifies which the body can hold onto the calories which it was missing before, plus fat gain usually happen. If you like to lose weight, eat healthy plus exercise. The weight can take longer to come off, nevertheless it might moreover be less likely to return.

Eat plenty of raw vegetables. Start a meal with lots of salad having carrots, peppers, celery, broccoli cucumber plus cabbage. Eating raw veggies can give you a feeling of fullness, causing you to eat less at standard food.

Once you're burning more calories then we will start to get rid of lose weight the fat. And how do you get you body to burn calories - with exercise plus exercising frequently.

Exercising first thing each morning gets rid of these feelings. You have finished before the day starts. We is happier because you'll learn that the rest of the day is free because you will have absolutely completed what we required to. There is no guilt and no dreading exercise because it may absolutely be completed.

We can follow different types of diets like Atkins diet, low-carb diet, high-protein diet, etc., and include the above-mentioned foods inside a diet plan to gain maximum advantages. All the best with your endeavor!

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