Immortal numbers

Immortality of Dual Numbers

Approximation for various powers at base 10, using immortal dual numbers with 1-5 digits and only positive parts;
2 is subtracted from the amount of integers in order to exclude the super immortal numbers 0 and 1:

$|\mathbb{M}^{power}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{true\ % dual\ numbers+integers-2}{{5}^{2}}$

$|\mathbb{M}^{2}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{0+10-2}{{5}^{% 2}}=0.32$

$|\mathbb{M}^{3}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{0+48-2}{{5}^{% 2}}=1.84$

$|\mathbb{M}^{4}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{0+10-2}{{5}^{% 2}}=0.32$

$|\mathbb{M}^{5}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{0+121-2}{{5}^% {2}}=4.76$

$|\mathbb{M}^{6}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{0+42-2}{{5}^{% 2}}=1.6$

$|\mathbb{M}^{7}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{0+48-2}{{5}^{% 2}}=1.84$

$|\mathbb{M}^{8}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{0+10-2}{{5}^{% 2}}=0.32$

$|\mathbb{M}^{9}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{0+158-2}{{5}^% {2}}=6.24$

$|\mathbb{M}^{10}_{10}|^{\mathbb{R}(\varepsilon)^{+}}\approx\tfrac{0+10-2}{{5}^% {2}}=0.32$