Database + Limit + Physics

How do you implement a database?

Database is a very large data. The data hierarchy goes from bit, to byte, to field, to record, to file or table, and then to database. There are also database of databases.
Implementing a database requires organizing the data in some fashion or pattern. The following describes 3 ways.
Sequential File Access Method: All records are organized sequentially using a key field as a unique record number for that record. An example would be a file of sequential records.
ISAM or Indexed Sequential Access Method: All records are also organized sequentially using a key field as a unique record number for that record. However, an indexed file is used to record the key field and its related address pointers to all the data in the record. An example would be a collection of related files stored in a disk which can be read by tracks instead of sequentially.
Random or Direct Access Method: All records can be stored sequentially or randomly in permanent storage using a key field as a unique record number for that record. But a record can be accessed randomly using a hashing formula or hash function or several hash functions that will yield the memory address pointers of each record data using the record's unique key field number. An example would be today's RDBMS systems.
Suggested websites:
https://en.wikipedia.org/wiki/ISAM
https://www.cs.cmu.edu/~adamchik/15-121/lectures/Hashing/hashing.html

What is the limit of a function in pre-calculus mathematics?

The limit of a function is the value of the range of a function, say y range, as the value of domain of the function, say x domain, approaches or reaches the specific x value. The limit of a function does not require the x value to be reached. So two things can happen when x is equal to the specific value. Either the function has a real y value at x value or the function has no y value at x value. If there is a real y value, then we do not have to use the limit of the function. If there is no real y value, then we can use the limit of a function to approximate a y value.
Now if we use the limit of a function, two things can happen. Either the function has a limit as it approaches the x value or we find the limit does not exist or is undefined because the y value has an indeterminate form value or the y value are actually 2 or more values for y, which makes it also undefined, because the definition of a function is there is only one range value for every domain value of a function.
Examples:
Limit of the function f(x) = 1/x as x approaches 0 is undefined. Substituting x with 0, we have 1/0, which is an indeterminate value. So let's try to approach x from both sides of the function. So we have 1/1 = 1 and 1/(-1) = -1. Since there are 2 values for y, the answer is undefined.
Limit of the function f(x) = x/2 as x approaches 2 is 1. Substituting x with 2, we have 2/2, which is equal to 1.
Limit of the function f(x) = 1/(x-2) as x approaches 2 is undefined. Substituting x with 2, we have 1/0. So let's try from both sides of the equation. So we have 1/(3-2) = 1/2 and 1/(1-2) = -(1/2). So the answer is also undefined.
Suggested website:
https://www.mathsisfun.com/calculus/limits.html

What is the fundamental of Physics?

This question is flawed. The correct question is "What are the fundamentals of Physics?". Because our knowledge of Physics is now humongous that there are many fundamentals that we need to know, and still many more to discover. But if you're not a physicist by profession, then you don't have to discover any of them or even know what is already discovered.
If this question was asked in the years with the suffix BC or BCE, i.e., Before Christian Era, then this question can be answered in one statement. The fundamental of Physics is the Archimedes' Principle, named after the Greek famous for yelling "Eureka!" in the nude.
This law of physics states that the opposing force exerted by a LIQUID on a fully or partially submerged SOLID body is equal to the WEIGHT of the displaced VOLUME of liquid. Written as a formula, it is F = pgV, where F is the force, p is the difference in density, g is the constant acceleration due to Earth's gravity, and V is the displaced Volume of liquid.
This law also explains why the huge Titanic was able to sail the Atlantic, but failed to do so when it was flooded by the additional weight of the cold Atlantic water. Brrr!
Suggested website:
http://formulas.tutorvista.com/physics/archimedes-principle-formula.html

Happy new semester Spring 2016!

John Sindayen