Quick question about induction

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    Induction
In summary, induction is a logical process of reasoning that involves making generalizations based on specific observations or examples. It is commonly used in science to formulate hypotheses and theories, make predictions, and test the validity of scientific theories. It differs from deduction, another type of logical reasoning, in that it moves from specific observations to general conclusions. However, there are limitations to induction, as the general conclusions may not always be accurate due to a limited number of observations and potential biases. Examples of induction in science include formulating the laws of gravity, developing the atomic theory, and understanding the process of evolution.
  • #1
Jamin2112
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Homework Statement



So my question i ...

Homework Equations



... when you're trying to prove some inequality, ...

The Attempt at a Solution



... for example, an < bn, can you do the inductive step by doing legal stuff to both sides of the inequality until you arrive at an+1 < bn+1?
 
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  • #2
My answer is...
what... is...
legal stuff ? XD ;-)

Do you have a specific example of what you mean ?
 
  • #3
╔(σ_σ)╝ said:
My answer is...
what... is...
legal stuff ? XD ;-)

Do you have a specific example of what you mean ?

I'm trying to prove that xn < xn+1, where x1 = √2 and xn+1 = √(2 + xn)
 

What is induction?

Induction is a logical process of reasoning that involves making generalizations based on specific observations or examples. It involves moving from specific cases to general principles or conclusions.

How is induction used in science?

In science, induction is used to formulate hypotheses and theories based on observations and experiments. It is also used to make predictions and test the validity of scientific theories.

What is the difference between induction and deduction?

Induction and deduction are two types of logical reasoning. Induction involves moving from specific observations to general conclusions, while deduction involves moving from general principles to specific conclusions.

What are some examples of induction in science?

Some examples of induction in science include observing the movement of planets and stars to formulate the laws of gravity, studying the behavior of atoms to develop the atomic theory, and examining fossils to understand the process of evolution.

What are the potential limitations of induction?

One limitation of induction is that the general conclusions drawn may not always be accurate or true. This is because induction relies on a limited number of observations and may not account for all possible variables. Additionally, the conclusions may be biased by personal beliefs or assumptions.

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