Prove 3/3 ≠ 1: Math Puzzle Challenge

Thread starter krypto
Start date Apr 13, 2005

In summary: Cauchy sequences of rationals and then mod out by the equivilance relation that two sequences are equivilant if the interpolated sequence is still Cauchy, then you get the reals. Now take the set of all Cauchy sequences of rationals whose terms are all eventually the same (i.e they converge to the same number). Then mod out by the equivilance relation that two sequences are equivilant if the interpolated sequence is still Cauchy and you get the set of reals that have terminating decimal expansions. We call these numbers "rational". Now take the set of all Cauchy sequences of rationals whose terms are all eventually the same

Apr 20, 2005

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

Well, since nobody seems to be learning anything, I'll close it up.

<h2>1. What is the math puzzle challenge "Prove 3/3 ≠ 1"?</h2><p>The math puzzle challenge "Prove 3/3 ≠ 1" requires you to use basic mathematical principles and operations to show that the fraction 3/3 is not equal to the whole number 1.</p><h2>2. Why is this puzzle challenging?</h2><p>This puzzle is challenging because at first glance, 3/3 and 1 may seem like they are equal. However, through careful mathematical reasoning, you can prove that they are not equal.</p><h2>3. What are some strategies for solving this puzzle?</h2><p>Some strategies for solving this puzzle include using basic arithmetic operations such as addition, subtraction, multiplication, and division, as well as properties of fractions and whole numbers.</p><h2>4. Can you provide an example of how to prove 3/3 ≠ 1?</h2><p>Yes, one way to prove 3/3 ≠ 1 is by using the property of equality which states that if two numbers are equal, then they can be substituted for each other in an equation. In this case, we can substitute 3/3 with 1, so the equation becomes 1 = 1. This is a true statement, showing that 3/3 and 1 are indeed equal.</p><h2>5. What is the significance of this puzzle in mathematics?</h2><p>This puzzle highlights the importance of understanding basic mathematical principles and operations and how they can be used to prove or disprove statements. It also demonstrates the power of logical reasoning and critical thinking in problem-solving.</p>

1. What is the math puzzle challenge "Prove 3/3 ≠ 1"?

The math puzzle challenge "Prove 3/3 ≠ 1" requires you to use basic mathematical principles and operations to show that the fraction 3/3 is not equal to the whole number 1.

2. Why is this puzzle challenging?

This puzzle is challenging because at first glance, 3/3 and 1 may seem like they are equal. However, through careful mathematical reasoning, you can prove that they are not equal.

3. What are some strategies for solving this puzzle?

Some strategies for solving this puzzle include using basic arithmetic operations such as addition, subtraction, multiplication, and division, as well as properties of fractions and whole numbers.

4. Can you provide an example of how to prove 3/3 ≠ 1?

Yes, one way to prove 3/3 ≠ 1 is by using the property of equality which states that if two numbers are equal, then they can be substituted for each other in an equation. In this case, we can substitute 3/3 with 1, so the equation becomes 1 = 1. This is a true statement, showing that 3/3 and 1 are indeed equal.

5. What is the significance of this puzzle in mathematics?

This puzzle highlights the importance of understanding basic mathematical principles and operations and how they can be used to prove or disprove statements. It also demonstrates the power of logical reasoning and critical thinking in problem-solving.