The discussion revolves around proving by contradiction that a real number which is less than every positive real number cannot itself be positive. Participants are exploring the implications of this statement within the context of real numbers.
There is ongoing exploration of the assumptions involved in the problem. Some participants are questioning the validity of a positive number being less than all positive numbers, while others are seeking hints to advance their reasoning.
Participants are reminded of forum rules that require them to demonstrate effort before receiving further assistance, indicating a focus on the learning process.
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?