RE: The Mathematical Proof Thread
October 1, 2016 at 4:11 pm
(This post was last modified: October 1, 2016 at 4:23 pm by Kernel Sohcahtoa.)
Here is one existence statement and one universally quantified statement that I came across. In order to prove an existence statement, simply find one example that makes the statement true. On the other hand, in order to disprove a universally quantified statement, find one example that makes the statement false.
Would anyone like to insert some quarters and play?
Tools
Definition of a prime number: A natural number n is prime if it has exactly two positive divisors, 1 and n.
Prime number calculator
Real numbers
1)There exist prime numbers p and q for which p-q=1,000
Hint
A Solution
2)The inequality 2^x is greater than or equal to x+1 is true for all positive real numbers x.
Hint
A Solution
References
Hammack, Richard. Book of Proof. Virginia: Richard Hammack (publisher), 2013.
Would anyone like to insert some quarters and play?
Tools
Definition of a prime number: A natural number n is prime if it has exactly two positive divisors, 1 and n.
Prime number calculator
Real numbers
1)There exist prime numbers p and q for which p-q=1,000
Hint
A Solution
2)The inequality 2^x is greater than or equal to x+1 is true for all positive real numbers x.
Hint
A Solution
References
Hammack, Richard. Book of Proof. Virginia: Richard Hammack (publisher), 2013.