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Which counterexample shows the conjecture is falseConjecture: The square of a rational number is greater than or equal to the number.?
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How do you write a conjecture about the sum of two fractions?
A conjecture is an opinion based on incomplete information, or a guess. It need not be true - or even sensible. So my conjecture is that the sum of two fractions is greater than three quarters. That is a nonsensical conjecture, but it is a conjecture and that is what the question requires.
Counterexample of the product of two positive numbers is greater than the sum of two numbers?
1x1=1 1+1=2
What is an example of goldbach's conjecture?
20 (which is an even # greater then 2)=7+13 (which are both prime #s)
What is Goldbach's conjecture?
Goldbach's Conjecture is that every even number greater than two can be expressed as the sum of two prime numbers. For example, 4 = 2 + 2, 6 = 3 + 3, 8 = 5 + 3, 10 = 7 + 3, 12 = 7 + 5, etc. Although the conjecture has been checked up to very large values and many weaker results have been proved, the conjecture remains open. Because it is so well-known and easily understood, it is frequently the subject of mistaken "proofs" by amateur mathematicians.
Is the product of two positive numbers greater than either number?
A positive number is any number greater than zero. 1 is a positive number, so is 2, 2.5, 3.14159, 11, 11.25 etc 0.5 is a positive number. The product of two positive numbers is the result of multiplying them together. * 2 x 3 = 6 (the product). In this case the product is greater than either number. But... * 0.5 x 0.25 is 0.125. ~In this case the product is actually smaller than either of the two numbers! * Or 0.5 x 10 = 5 . Here the product is greater than 0.5 but smaller than 10. So the answer is ...sometimes!
