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From Wikipedia

Constant problem

In mathematics, the constant problem is the problem of deciding if a given expression is equal to zero.

The problem

This problem is also referred to as the identity problem or the method of zero estimates. It has no formal statement as such but refers to a general problem prevalent in transcendence theory. Often proofs in that field of maths are contradiction proofs, specifically they use some auxiliary function to create an integer n&nbsp;&ge;&nbsp;0 which is shown to satisfy n&nbsp;<&nbsp;1. Clearly this means that n must have the value zero, and so a contradiction arises if one can show that in fact n is not zero.

In many transcendence proofs, proving that n&nbsp;≠&nbsp;0 is very difficult, and hence a lot of work has been done to develop methods that can be used to prove the non-vanishing of certain expressions. The sheer generality of the problem is what makes it difficult to prove general results or come up with general methods for attacking it. The number n that arises may involve integrals, limits, polynomials, other functions, and determinants of matrices.

Results

In certain cases algorithms or other methods exist for proving that a given expression is non-zero, or of showing that the problem is undecidable. For example, if x1,&nbsp;...,&nbsp;xn are real numbers then there is an algorithm for deciding if there are integers a1,&nbsp;...,&nbsp;an such that

|a_1 x_1+{}\cdots{}+a_n x_n|=0.\,

If the expression we are interested in contains a function which oscillates, such as the sine or cosine function, then it has been shown that the problem is undecidable, a result known as Richardson's theorem. In general, methods specific to the expression being studied are required to prove that it cannot be zero.



From Yahoo Answers

Question:Please explain how to estimate by using front end estimation 546-234 Do I need to round off to the nearest....? Please help and thanks

Answers:I would loosely say 550 - 250 = 300; .... or 540 - 240 = 300 whereas actual answer = 312 ... so semi-close and in the ballpark. if you could get closer, you would probably be able to do the actual problem in your head.

Question:My daughter has been working in math on estimation and rounding. (3rd grade) She brought home an assignment on Front end estimation. I understand the concept ex: 789 + 545 = 700 + 500 But why would you use it? It seems so much more natural to use regular estimation/rounding and it seems like regular estimation and round would give you a more correct estimate. When would you use this as opposed to regular estimation?

Answers:I have no idea. One of the teachers I worked with even admitted that some of the things that they teach won't be used that much if at all in the real world, and that only certain occupations will use certain things. Call her up and ask her.

Question:Its for my 6th grade math class. I looked every were but i cant find a definition.

Answers:Front end estimation mostly produces a closer estimate of sums or differences than the answer produced by adding or subtracting rounded numbers. How to estimate a sum by front end estimation: Add the digits of the two highest place values Insert zeros for the other place values Example 1: 4496 + 3745 is estimated to be 8100 by front end estimation (i.e. 4400 + 3700). Example 2: 4496 + 745 is estimated to be 5100 by front end estimation (i.e. 4400 + 700). ------------------------------- Using the leading, or left-most, digits to make an estimate quickly and easily. Example:Using front-end estimation to estimate the sum of 594, 32, and 221, an initial estimate would be 5 + 0 + 2 hundreds or 700.

Question:I have a 1998 nissan sentra. Getting a vibration on the steering, and car, taught it was the rims / tires damaged, (i had 17"rims, nexen tires on the car). Last week I had NEW RIMS, and TIRES installed, alligned and balanced, and still a major vibration on the front end of the car when i take my foot off of the accellarator. This only happens at speeds above 100km. Can anyone suggest a cause/ solution?

Answers:Seems to be an alignment problem if it only happens at high speed. But it could also be a whole range of other issues, possibly to do with your suspention. I suggest you take to a professional to get it sorted. Also dont drive too fast, getting your license taken away isnt fun ;)

From Youtube

Estimating with Whole Numbers :This video explains how to estimate addition, subtraction, multiplication, and division math problems by using rounding and compatible numbers. For additional free homework help visit us at www.thefreetutor.com