c - enum: why can two different enumeration-constants have the same integer value? -

I know that if I have defined an enum weekday like this:

  Enum weekday {mon, tue, wed, thu, fa,};   
 Then, the mon will be internally equal to 0, by default, and 1, from WED to WED 2 ...  
 But if I do it like this I define: / P> 
  enum weekdays {mon, teie = 0, wade, thu, fa,};   
 Then both the  MON  and  TUE  will get the value of 0.  
 How different will the system be internal and TUE? I mean, if I declare something like this:  
  today's day = 0;   
 So today is  mon  or  TUE ? Or, both philosopher-speaking, 
 
 
 C enums are "in fact" integers - not just because they are implemented in such a way , But because standard  defines  enum types have integer values, then  today's value is "actually" 0. Whatever has happened is that you have two variations for value 0 Names have been created.  
 I think the answer is "Today is MON or TEE" "Yes"; -)  
 The language can not stop you because sometimes it is useful for many names of the same value for the value. For example:  
  enum compression_method {COMP_NONE = 0, COMP_LOW = 1, COMP_HIGH = 2, COMP_BEST = 2, COMP_FASTEST = 0,};