Marlins0412
Explain Irrational numbers and give a few examples Thanks!
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inkyvoyd
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A rational number is a number that can be expressed as the ratio of two integers. For instance, 0.5 is a rational number, which is 1/2
inkyvoyd
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0.394 repeating can be expressed as 394/999
Marlins0412
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ok so how many irrational numbers are from 1-10?
Marlins0412
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Im studying for my ACT test tomorrow
inkyvoyd
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However, in the defined "real number set", not all numbers can be expressed as the division of two integers. Although historically it took a bit of time for us to accept this, a simple proof of the the fact that \(\sqrt{2}\) is irrational is suffice
inkyvoyd
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There are an infinite number of rational AND irrational numbers between 1-10...
Marlins0412
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give me an example why please
inkyvoyd
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Well, pick two numbers between 1 and 10.
Marlins0412
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2 and 7
inkyvoyd
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Pick two numbers in between those two.
Marlins0412
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5, 6
inkyvoyd
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Now do it again.
Marlins0412
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5.6, 5.7
inkyvoyd
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an important property of the real numbers is that they are continuous - in a sense, there are an INFINITE "number" of numbers in between any two different numbers, no matter how small the difference
inkyvoyd
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There are actually "far more" irrational numbers than rational numbers.
Marlins0412
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so in 1-3 there is many aswell?
inkyvoyd
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Well, comparing the two expressions is indeterminant I believe
Marlins0412
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Great! Thanks a lot for your help it cleared my confusion. Hopefully I get this right on one of the biggest tests of my life!
inkyvoyd
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@Marlins0412 , the key thing to know is that there are an infinite number of rational and irrational numbers
inkyvoyd
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rational numbers can be expressed as the division of two integers, while irrational numbers cannot
Marlins0412
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I see
Marlins0412
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WEll off to more studying thanks again
inkyvoyd
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yes - good luck!
Marlins0412
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Thanks so much!