# Warning to New Users: There are 7 kinds of numbers in Mathematica

Posted 8 years ago
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 Integers (Infinite Precision), Reals (Infinite Precision, Machine Precision, Arbitrary Precision), Complexes ((Infinite Precision, Machine Precision, Arbitrary Precision) with some overlap. That's why the square root of 2 returns the square root of two, to maintain the precision. In[1]:= Element[1, Integers] Out[1]= True In[2]:= Precision[1] Out[2]= \[Infinity] In[3]:= Element[2/3, Reals] Out[3]= True In[4]:= Precision[2/3] Out[4]= \[Infinity] In[11]:= Sqrt[2] Out[11]= Sqrt[2] In[10]:= Precision[Sqrt[2]] Out[10]= \[Infinity] In[6]:= Precision[1.0] Out[6]= MachinePrecision In[7]:= Precision[N[1, 25]] Out[7]= 25. In[9]:= Element[2, Complexes] Out[9]= True In[8]:= Element[2 + 3 I, Complexes] Out[8]= True In[12]:= Precision[2 + 3 I] Out[12]= \[Infinity] In[13]:= Precision[N[2 + 3 I, 25]] Out[13]= 25. 
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