datetime values appear to be equal but return not equal

I have two datetime variables that appear to be the same (even using format long), but matlab says they are not equal:

Any idea what's going on here? I discovered this because the setxor function told me these values were mutually exclusive.

K>> T1(1)
ans = 
  datetime
   24-Aug-2020 18:00:01.730
K>> T2(2)
ans = 
  datetime
   24-Aug-2020 18:00:01.730
K>> datenum(T1(1))
ans =
     7.380277500200346e+05
K>> datenum(T2(2))
ans =
     7.380277500200346e+05
K>> isequal(T2(2),T1(1))
ans =
  logical
   0

Answer 1

[John D'Errico]

format long does NOT tell you every single digit in the number!!!!

format long does NOT tell you every single digit in the number!!!!

format long does NOT tell you every single digit in the number!!!!

There, I've said it three times, so it must be true.

format long
X = pi

X = 
   3.141592653589793

Y = X - 3.e-16

Y = 
   3.141592653589793

Do they appear to be identical? Yes. Down to the last digit, I think. At least, format long tells me so. But are they?

X == Y

ans = logical
   0

Numbers are stored with a 52 bit mantissa in MATLAB. However, 52 binary bits is how many decimal digits? There is not an integer relationship between binary bits and decimal digits. So while format long gives you DECIMAL digits, you don't see the exact bits.

Answer 2

[Steven Lord]

What does this show you?

seconds(T2(2)-T1(1))

That will likely be small enough to make no difference in how those datetime values are displayed but large enough to make them not return true for the equals calculation.

[Dan Klisiewicz]

K>> T1(1)-T2(2)
ans = 
  duration
   00:00:00

[Steven Lord]

You forgot the seconds call.

T1 = datetime('now')

T1 = datetime
   01-Apr-2021 18:10:05

T2 = T1 + seconds(1e-4)

T2 = datetime
   01-Apr-2021 18:10:05

T2-T1

ans = duration
   00:00:00

seconds(T2-T1)

ans = 1.0000e-04