# Any help understanding this Lemma is Appreciated

• Mining_Engr
In summary, a Lemma is a statement or proposition used to prove a larger theorem, and understanding its role can be helpful in breaking down complex problems. Lemmas can be used to prove multiple theorems and are not limited to mathematics, as they are used in various fields of science and research. To improve understanding, one can read through the proof and practice applying Lemmas to different scenarios.
Mining_Engr
The lemma and proof are attached, how does the hypothesis imply that ∫h(u)*p(u)du = 0. This is where I am hung up. I don't see how the hypothesis implies this, please help!

Mining_Engr

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p(u) is a polynomial, say
$$p(u) = \sum_{i=0}^n \alpha_i u^i$$

then
$$\int h(u) p(u) du = \int h(u) \sum_{i=0}^n \alpha_i u^i du = \sum_{i=0}^n \alpha_i \int h(u) u^i du$$
and all those integrals at the end are zero so the whole sum is zero

## 1. What is a Lemma?

A Lemma is a statement or proposition that is used as a stepping stone to prove a larger theorem or proposition. It is often a smaller, more specific version of the larger statement.

## 2. How can understanding a Lemma be helpful?

Understanding a Lemma can be helpful because it provides a starting point for tackling a larger problem or concept. It breaks down a complex statement into smaller, more manageable pieces.

## 3. Can a Lemma be used to prove multiple theorems?

Yes, a Lemma can be used to prove multiple theorems. This is because Lemmas are often general statements that can be applied to different scenarios or problems.

## 4. Are Lemmas only used in mathematics?

No, Lemmas can be used in various fields of science and research, not just in mathematics. They are commonly used in computer science, physics, and engineering, among others.

## 5. How can I improve my understanding of a Lemma?

To improve your understanding of a Lemma, you can read through its proof and try to identify the key concepts and logic used. You can also practice applying Lemmas to different problems to gain a better understanding of how they work.

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