let me see if i understand, x is in [0,1] then f(x) is in [1,2] therefore f:x->f(x) therefore the number of rationals in [0,1] equals to [1,2].Originally posted by master_coda
To show that the number of rationals on [0,1] is the same as the number of rationals on [1,2] you just need to find a bijection from [0,1] to [1,2].
Clearly [itex]f(x)=x+1[/itex] is a suitable bijection.
When two domains are equal to each other, it means that they have the same elements or values. In other words, they are identical or have no difference between them.
Yes, there can be significance to two domains being equal. It can indicate a relationship or connection between the two domains, or it can provide evidence for a mathematical or scientific theory.
Yes, two domains that are equal can have different names. This is because the names of domains are simply labels or identifiers, and do not affect the actual elements or values within the domain.
To determine if two domains are equal, you need to compare their elements or values. If they have the same elements or values, then they are equal. This can be done through mathematical or scientific methods, such as set theory or statistical analysis.
Yes, two domains can be equal but have different sizes. This can occur if the domains have the same elements, but the elements are arranged or organized differently. For example, two sets of numbers can have the same elements, but one set may be in ascending order while the other is in descending order.