. The infinite dihedral group D[infinity] is a subgroup of permutations of the integers generated by f(n) = −n and g(n) = 1 − n, which reflect the integer number line over the point 0 and 1/2 respectively. (a) Give a presentation of D[infinity]. (b) Demonstrate a surjective homomorphism to each finite dihedral group ϕ : D[infinity] → Dn for n ≥ 3.

2 and 1.

step-by-step explanation:

plug in each answer. 0 doesn't work, 1 does. so does 2. 4 doesn't:

0 = 1 is not true.

2 = 2 is true.

4 = 4 is true.

8 = 16 is not true.

hope this !

true

step-by-step explanation:

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870

a_n = a_1 + (n - 1)d

the first term is 6.

the common difference d = ?

when you find d, replace n with 7 and d with the common difference to find your answer.