# Pie?

$$\pi$$ and $$e$$ are both transcendental numbers. Transcendental numbers are numbers which can't be roots of a non-zero polynomial equation with rational coefficients. Keeping that in mind, read the following statements.

$$[1]$$. It is possible for $$\pi+e$$ to be a rational number in base $$10$$.

$$[2]$$. At least one of $$\pi+e$$ and $$\pi \times e$$ is irrational in base $$10$$.

$$[3]$$. $$\pi$$ is an irrational number in base $$10$$.

Which of these statements are correct?

Note: This problem is a part of the set "I Don't Have a Good Name For This Yet". See the rest of the problems here. And when I say I don't have a good name for this yet, I mean it. If you like problems like these and have a cool name for this set, feel free to comment here.

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