Answer:
[tex]\large \boxed{800}[/tex]
Step-by-step explanation:
A cardinal number is the number of distinct elements in a finite set.
Your set consists the integers from 208 to 1007.
Each element is 1 more than the preceding element, so it represents an arithmetic sequence with distinct elements.
The formula for the nth term in an arithmetic sequence is
aₙ = a₁ + (n - 1)d, where
a₁ = the first element of the sequence
n = the common difference between successive terms
In your sequence,
a₁ = 208 and d = 1
To figure out how many elements are in the set, set aₙ to 1007 — the last member — and solve for n.
[tex]\begin{array}{rcl}a_{n} & = & a_{1} + (n - 1)d\\1007 & = & 208 + (n - 1) \times 1\\1007 & = &208 + n - 1\\1007 & = &207 + n\\n & = & \mathbf{800}\\\end{array}\\\text{The cardinal number is $\large \boxed{\mathbf{800}}$}[/tex]
