- #1
Simple Identity Proof for Homework | Equations & Solution Attempt
In summary, a proof by simple identity is a type of mathematical proof that shows two expressions are equal using basic algebraic operations and the concept of identity. It is applicable when the expressions are identical or can be manipulated to become identical. The steps for constructing a proof by simple identity include identifying the expressions, manipulating them, stating the equality based on identity properties, and providing justifications. This type of proof can be used in any branch of mathematics, but common mistakes to avoid include assuming equality without proper steps and using incorrect algebraic manipulations.
- #2
HallsofIvy
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I take it that what you have in "The attempt at a solution",
[tex]x^n\le a_0+ a_1x+ a_2x^2+ \cdot\cdot\cdot+ a_{n-1}x^{n-1}[/tex]
is actually what you want to prove. I cannot open the first attachment. But that is certainly NOT true for general x, [itex]a_0[/itex], [itex]a_1[/itex], ... So what are you really trying to do?
[tex]x^n\le a_0+ a_1x+ a_2x^2+ \cdot\cdot\cdot+ a_{n-1}x^{n-1}[/tex]
is actually what you want to prove. I cannot open the first attachment. But that is certainly NOT true for general x, [itex]a_0[/itex], [itex]a_1[/itex], ... So what are you really trying to do?
- #3
Related to Simple Identity Proof for Homework | Equations & Solution Attempt
1. What is a proof by simple identity?
A proof by simple identity is a type of mathematical proof that uses the concept of identity to show that two expressions are equal. This type of proof is commonly used in algebra and calculus.
2. How do you identify when a proof by simple identity is applicable?
A proof by simple identity is applicable when two expressions are identical or can be manipulated to become identical through basic algebraic operations such as addition, subtraction, multiplication, and division.
3. What are the steps for constructing a proof by simple identity?
The steps for constructing a proof by simple identity are as follows:
- Identify the two expressions that need to be proven equal.
- Manipulate the expressions using basic algebraic operations to make them identical.
- State that the two expressions are equal based on the properties of identity.
- Provide a reason or explanation for each step of the proof.
4. Can a proof by simple identity be used in any branch of mathematics?
Yes, a proof by simple identity can be used in any branch of mathematics where the concept of identity is applicable, such as algebra, calculus, and trigonometry.
5. Are there any common mistakes to avoid when constructing a proof by simple identity?
Yes, some common mistakes to avoid when constructing a proof by simple identity are:
- Assuming that the two expressions are equal without showing the steps to reach that conclusion.
- Using incorrect or invalid algebraic manipulations.
- Not providing proper justifications for each step of the proof.
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