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The names x_i indicate the order in which the variables x[i] are accessed first. You can see it if you set parameter name of method new_variable.

sage: p = MixedIntegerLinearProgram(maximization=False, solver="GLPK") 
....: x = p.new_variable(real=True, nonnegative=True, name="x") 
....: p.set_integer(x[2]) 
....: p.add_constraint(2*x[0] + 2*x[1] + 3*x[2] - 10*x[3] <= 0) 
....: p.add_constraint(6*x[1] + 4*x[2] - 11*x[3] >= 0) 
....: p.add_constraint(2*x[2] - 6*x[3] <= 0) 
....: p.add_constraint(x[0] - x[1] - x[2] >= 0) 
....: p.add_constraint(x[3] >= 1) 
....: p.set_objective(3*x[1] + 6*x[2] - 3*x[3]) 
....: p.show()                                                                                                                      
Minimization:
  6.0 x[2] + 3.0 x[1] -3.0 x[3] 

Constraints:
  3.0 x[2] + 2.0 x[0] + 2.0 x[1] - 10.0 x[3] <= 0.0
  -4.0 x[2] - 6.0 x[1] + 11.0 x[3] <= 0.0
  2.0 x[2] - 6.0 x[3] <= 0.0
  x[2] - x[0] + x[1] <= 0.0
  - x[3] <= -1.0
Variables:
  x[2] = x_0 is an integer variable (min=0.0, max=+oo)
  x[0] = x_1 is a continuous variable (min=0.0, max=+oo)
  x[1] = x_2 is a continuous variable (min=0.0, max=+oo)
  x[3] = x_3 is a continuous variable (min=0.0, max=+oo)

The names x_i indicate the order in which the variables x[i] are accessed first. You can see it if you set parameter name of method new_variable. So variable x[2] is correctly sets to integer, although it's internal name is x_0.

sage: p = MixedIntegerLinearProgram(maximization=False, solver="GLPK") 
....: x = p.new_variable(real=True, nonnegative=True, name="x") 
....: p.set_integer(x[2]) 
....: p.add_constraint(2*x[0] + 2*x[1] + 3*x[2] - 10*x[3] <= 0) 
....: p.add_constraint(6*x[1] + 4*x[2] - 11*x[3] >= 0) 
....: p.add_constraint(2*x[2] - 6*x[3] <= 0) 
....: p.add_constraint(x[0] - x[1] - x[2] >= 0) 
....: p.add_constraint(x[3] >= 1) 
....: p.set_objective(3*x[1] + 6*x[2] - 3*x[3]) 
....: p.show()                                                                                                                      
Minimization:
  6.0 x[2] + 3.0 x[1] -3.0 x[3] 

Constraints:
  3.0 x[2] + 2.0 x[0] + 2.0 x[1] - 10.0 x[3] <= 0.0
  -4.0 x[2] - 6.0 x[1] + 11.0 x[3] <= 0.0
  2.0 x[2] - 6.0 x[3] <= 0.0
  x[2] - x[0] + x[1] <= 0.0
  - x[3] <= -1.0
Variables:
  x[2] = x_0 is an integer variable (min=0.0, max=+oo)
  x[0] = x_1 is a continuous variable (min=0.0, max=+oo)
  x[1] = x_2 is a continuous variable (min=0.0, max=+oo)
  x[3] = x_3 is a continuous variable (min=0.0, max=+oo)