No.
1-ε/2 is the largest number below 1. 1+ε is the smallest number above 1.
The significand for a normalized floating-point number is always in the range [1,2). Therefore, to represent numbers in the range [0.5,1), the exponent is -1 and the LSB is half as large.
So in binary, 1 + ε is something like:
1 + ε = 1.000...0001 ⨯ 20
You can see that there's no number between 1 and 1 + ε, which matches the definition for ε.
But 1 - ε is something like:
1 - ε = 1.111...1110 ⨯ 2-1
So there is exactly one number between 1 - ε and 1, that is, 1 - ε/2.