Is it a real number?

Number Theory Level 3

True or False:-

The number below is not a real number

1 1 1 1 1 1 1 1 ⋯ \large11^{11^{11^{11^\cdots}}}

True False

Shreyansh Mukhopadhyay by Shreyansh Mukhopadhyay , 18, India

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1 solution

Let 1 1 1 1 1 1 1 1 ⋯ = x \large11^{11^{11^{11^\cdots}}}=x

Then we have 1 1 x = x \large11^x=x

But on drawing the graph for y = 1 1 x and y = x y=11^x \text{ and }y=x , we find the two graphs never meet.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Something seems a little strange; one would think the exponentiation would increase without bound. Ed Gray

Edwin Gray - 2 years, 5 months ago

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