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by Simply Pengu on October 10th, 2011

Simply Pengu

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how do we add irrational numbers?

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  • by xprofessor on October 11th, 2011

    xprofessor

    Addition is well-defined for all real numbers. It's just that irrationals can't be expressed as simple decimals or fractions (they have an infinitely long non-repeating series of decimal digits) so their sum might not have a simple notation the way rational numbers do.

    For example, we can compute that (1/2 + 1/3) can be simplified as 5/6. But (√2 + √3) is already in simplest terms. Some sums of irrationals, of course, can be simplified. For example, if a = √2+1 and b = √2-1, then a+b = √2.

    The "problem" with adding irrational numbers isn't with the numbers themselves, it's just with our limited system of notation for writing them down.

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