query: Which one is bigger, $e ^ {3 \pi}$ or $ \space 3 ^ {e \pi}$?
positive_passages.docid: 156541
positive_passages.text: $a^b > b^a$ or $a^b b$ where $a,b$ are positive real numbers
negative_passages.docid: 48598
negative_passages.text: What's the difference between $\mathbb{R}^2$ and the complex plane?
negative_passages.docid: 116616
negative_passages.text: Could $X^3 + X + 1$ have a root in $E?$
negative_passages.docid: 85311
negative_passages.text: Proving that $e^{\pi}-{\pi}^e\lt 1$ without using a calculator
negative_passages.docid: 62506
negative_passages.text: Why $SU(3)$ and not $U(3)$?
negative_passages.docid: 116168
negative_passages.text: Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$?
negative_passages.docid: 42372
negative_passages.text: Space Expansion vs. Relative Motion
negative_passages.docid: 103616
negative_passages.text: Distance between powers of 2 and 3
negative_passages.docid: 53583
negative_passages.text: Why $e^x$ is always greater than $x^e$?
negative_passages.docid: 30404
negative_passages.text: Is $\mathbb{Z}/3\otimes \mathbb{Z}[1/2]=\mathbb{Z}/3$?
negative_passages.docid: 126040
negative_passages.text: Geometric explanation of $\sqrt 2 + \sqrt 3 \approx \pi$
negative_passages.docid: 138944
negative_passages.text: Is $\mathbb Z[\sqrt{-3}]$ Euclidean under some other norm?
negative_passages.docid: 35454
negative_passages.text: Is it correct to write $\Bbb E[X]$ or $\Bbb E_{\theta}[X]$?
negative_passages.docid: 100968
negative_passages.text: Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
negative_passages.docid: 96805
negative_passages.text: Why is the Absolute Value of $3-π$ equal to $π - 3$
negative_passages.docid: 95145
negative_passages.text: Does $\exp(2ir\pi)$ equal $1$? What's wrong?
negative_passages.docid: 60721
negative_passages.text: How does $e^{i x}$ produce rotation around the imaginary unit circle?