Discrete Math: Proving a Homework Statement

In summary, the conversation is discussing how to prove the statement that 2^(1/x) approaches 1 as x approaches infinity. The conversation explores different approaches, including using the definition of limit and solving the equation 2^(1/x) = r, and mentions graphing as well. The conclusion is that the statement is true and can be proven using mathematical concepts.
  • #1
planauts
86
0

Homework Statement


http://puu.sh/1OfE2

Homework Equations


The Attempt at a Solution


I am not really sure about this one! :(
I think it's 1 because
http://puu.sh/1OfY0
http://puu.sh/1OfYE

I came up the number by working backwards (assuming the conclusion is true). However, for a proof, I cannot assume the conclusion is true and try proving the hypothesis. Could someone nudge me to the right direction in proving this statement?

Thanks!
 
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  • #2
As you say,
[tex]\lim_{x \to \infty} 2^{\frac{1}{x}} = 1[/tex]
But since this is discrete mathematics, perhaps it's more intuitive to define an = 21/n and write
[tex]\lim_{n \to \infty} a_n = 1[/tex]

Now can you solve it if I say: "[itex]r = 1 + \epsilon[/itex]" and "definition of limit"?
 
  • #3
No, I don't understand the second part with epsilon.
 
  • #4
Do you know what the definition of the limit is?
 
  • #5
Consider n<0
 
  • #6
When I graphed it, i found out that r > 0.5 because 2^(-1) is 0.5 since n has to be int and -1 is an int but i don't know how to prove it. Graphing is not a good way, according to my Prof.
 
  • #7
If you haven't learned the definition of limit yet, another approach is as follows: try solving the equation 2^(1/x) = r first. Once you find x for which the equality holds, you can may use your graph for inspiration for an integer n such that the inequality holds.
 

Related to Discrete Math: Proving a Homework Statement

What is discrete math?

Discrete math is a branch of mathematics that deals with objects that can only take on distinct, separate values. It is often used in computer science and other fields to solve problems that involve counting, logic, and algorithms.

What does it mean to prove a statement in discrete math?

To prove a statement in discrete math means to use logical reasoning and mathematical techniques to show that the statement is always true. This involves breaking down the statement into smaller, simpler parts and using known mathematical principles to demonstrate its validity.

What are some common techniques used to prove statements in discrete math?

Some common techniques used to prove statements in discrete math include mathematical induction, direct proof, proof by contradiction, and proof by contrapositive. These techniques involve using logical arguments and mathematical principles to show that a statement is always true.

Why is it important to prove statements in discrete math?

Proving statements in discrete math is important because it allows us to ensure the accuracy and validity of mathematical theories and algorithms. It also helps us to better understand the underlying principles and patterns involved in solving a problem, which can lead to more efficient and effective solutions.

What are some tips for effectively proving a statement in discrete math?

Some tips for effectively proving a statement in discrete math include carefully reading and understanding the statement, breaking it down into smaller parts, using known mathematical principles and techniques, and providing clear and logical reasoning for each step. It is also important to check for any potential errors or counterexamples in the proof.

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