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Proof by contradiction

  • Thread starter zoxee
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  • #1
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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?
 

Answers and Replies

  • #2
pasmith
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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?
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]?
 
  • #3
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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]?
I'm sorry but I can't seem to proceed even with this hint :(
 
  • #4
pasmith
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I'm sorry but I can't seem to proceed even with this hint :(
Given that [itex]x[/itex] is a positive real number, is [itex]x/2[/itex] a positive real number?
 
  • #5
HallsofIvy
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I wouldn't even bother with x/2. Suppose x is positive. Can it then be "less than every positive number"
 
  • #6
berkeman
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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?
Please check your PMs. The PF Rules require that you show some effort before we offer tutorial help.
 

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