zoxee said:Prove by contradiction that a real number that is less than every positive real number cannot be positive
having troubles with this
could someone give me a small hint to get started?
pasmith said:Suppose [itex]x > 0[/itex] is such that every positive real number is greater than or equal to [itex]x[/itex]. What then is [itex]x/2[/itex]?
zoxee said:I'm sorry but I can't seem to proceed even with this hint :(
zoxee said:Prove by contradiction that a real number that is less than every positive real number cannot be positive
having troubles with this
could someone give me a small hint to get started?
"Proving Negative Real Numbers Using Contradiction" is a mathematical method used to prove that a number is negative by assuming the opposite (that it is positive) and showing that it leads to a contradiction.
"Proving Negative Real Numbers Using Contradiction" is important because it allows us to prove the existence of negative real numbers, which are crucial in many mathematical concepts and real-life applications. It also helps to strengthen our understanding of mathematical proofs and logic.
"Proving Negative Real Numbers Using Contradiction" works by assuming that the number in question is positive and then using mathematical operations and logical arguments to arrive at a contradiction, thus proving that the number must be negative. This method is based on the principle of proof by contradiction.
The main difference between these two methods is the starting assumption. In "Proving Negative Real Numbers Using Contradiction", we assume that the number is positive and try to reach a contradiction, while in "Proving Positive Real Numbers Using Contradiction", we assume that the number is negative and try to reach a contradiction.
Yes, there are limitations to this method. It may not work in every scenario and may require additional assumptions or conditions to be proven. It also relies on the concept of proof by contradiction, which may not be applicable in all mathematical proofs. Furthermore, it may not be the most efficient method in some cases and may require a lot of steps and calculations.