All you proved is that x in not an integer.charmedbeauty said:
This statement is false. x=0 is a counterexample: it satisfies the hypothesis, but not the conclusion.
For this bit, I can't tell if there's any problem with your reasoning, because you don't say what you're reasoning is -- you just wrote two equations.
The notion of "even" and "odd" applies to integers, but it doesn't apply to real numbers. If you are using x to denote a real number, then 2x2 is also 'merely' a real number, and so it doesn't make sense to talk about it being even.
This is another false statement. x=0 is another counterexample. It is real, however it is not irrational. It also has nothing to do with the statement you said you were trying to prove.
Hurkyl said:There are many things wrong.
This statement is false. x=0 is a counterexample: it satisfies the hypothesis, but not the conclusion.
For this bit, I can't tell if there's any problem with your reasoning, because you don't say what you're reasoning is -- you just wrote two equations.
The notion of "even" and "odd" applies to integers, but it doesn't apply to real numbers. If you are using x to denote a real number, then 2x2 is also 'merely' a real number, and so it doesn't make sense to talk about it being even.
This is another false statement. x=0 is another counterexample. It is real, however it is not irrational. It also has nothing to do with the statement you said you were trying to prove.
I hate to say it, but I think what you need to do is to focus on trying to understand logic, grammar, and the meaning of what you read/write, and also on explicitly writing out what you are thinking and doing.
Would you please state exactly the question you were asked? I'm guessing it's something similar to
If x is a real number satisfying the equation 2x2 - 3 = 0, then x is irrational.Once you've stated the question, it may be useful to do one or all of the following:
- Explain why your statement in the opening post means the same thing or doesn't mean the same thing as the question you were asked.
- Explain why my statement means the same thing or doesn't mean the same thing as the question you were asked.
- Explain why my statement means the same thing or doesn't mean the same thing as your statement in the opening post.
Office_Shredder said:
HallsofIvy said:
An irrational number is a real number that cannot be expressed as a ratio of two integers. This means that it cannot be written as a simple fraction and the decimal representation of an irrational number is non-terminating and non-repeating.
To prove the irrationality of a number, one must show that it cannot be expressed as a ratio of two integers. This can be done by using proof by contradiction or by showing that the number has an infinite number of non-repeating decimal digits.
Yes, irrational numbers can be calculated using mathematical operations such as addition, subtraction, multiplication, and division. However, the result may not be a precise value and may involve an infinite number of decimal digits.
Yes, all square roots of non-perfect squares are irrational numbers. This can be proven by showing that the decimal representation of the square root is non-terminating and non-repeating, which is a characteristic of irrational numbers.
Irrational numbers are used in various fields of science, including physics, chemistry, and biology. They are often used in mathematical models to represent natural phenomena and in calculations involving measurements with infinite decimal places. In physics, irrational numbers are used to describe quantities such as the ratio of a circle's circumference to its diameter, which is the irrational number pi (π).