# Do any terms in mathematics exist to describe these concepts?

If you have already waited 20 minutes for the bus, the bus can not arrive in less than 20 minutes because you can not "un-wait" the time you have already waited.

If you have 5 donuts and you eat some donuts - it is impossible to have more than 5 donuts when you are finished eating. This is because once you remove items from a set, the set can not have more items than the original number of items in the set.

If you walked 345 meters by 6 PM, the total number of meters you will have walked today can not be less than 345 meters. This is because you can not "un-walk" the meters you have already walked.

Do these concepts have proper names in math? E.g Commutative, reflexive, symmetric, etc? How would you describe this property using mathematical terms - a set of objects that have certain properties, such that once a certain type of opperation is performed on objects in the set, the "cardinality" of set achieves a new infimum and supremum?

Do such terms in mathematics exist that can correspond to the examples I laid out?

Thanks!

• "Properties" in math do not change over time... Thus, you have to index the above properties with a specific point in time: the set of donuts at time 1 has 5 donuts while the set of donuts at time 1 (after eating) has less than 5 donuts. Jan 17 at 9:51
• Wait times, donuts, or walk lengths are not math. But if you can measure them, you can translate those into math relations, and order theory might be relevant.
– dxiv
Jan 17 at 9:56
• For a reason , I would say that there are objects that cannot be negative, like time , length or the number of objects. I remember this joke : If $3$ people are in a bus and $5$ leave it , then $2$ people must enter the bus to make it empty :) Jan 17 at 9:57

Well, we could say that if $$x$$ is the number of meters you will have walked by the end of the day, then $$x \in [345, \ m]$$, where $$m$$ is some theoretical maximum that you can't possibly exceed in a day. This interval has a "minimum value" of 345 which is, as you say, "the total number of meters you will have walked today can not be less than".