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In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences.
Loop (topology) Two loops a, b in a torus. In mathematics, a loop in a topological space X is a continuous function f from the unit interval I = [0,1] to X such that f(0) = f(1). In other words, it is a path whose initial point is equal to its terminal point. [1] A loop may also be seen as a continuous map f from the pointed unit circle S1 into ...
Conjecturally, this inverse relation forms a tree except for a 1–2 loop (the inverse of the 1–2 loop of the function f(n) revised as indicated above). Alternatively, replace the 3 n + 1 with n ′ / H ( n ′ ) where n ′ = 3 n + 1 and H ( n ′ ) is the highest power of 2 that divides n ′ (with no remainder ).
v. t. e. In computer science, a for-loop or for loop is a control flow statement for specifying iteration. Specifically, a for-loop functions by running a section of code repeatedly until a certain condition has been satisfied. For-loops have two parts: a header and a body. The header defines the iteration and the body is the code that is ...
t. e. A feedback loop where all outputs of a process are available as causal inputs to that process. Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. [ 1 ] The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled ...
Recursion is the process a procedure goes through when one of the steps of the procedure involves invoking the procedure itself. A procedure that goes through recursion is said to be 'recursive'. [ 3 ] To understand recursion, one must recognize the distinction between a procedure and the running of a procedure.
First "push" the loop into a three-dimensional subspace, which is always possible, though technical to explain. Four-dimensional space occurs in classical knot theory, however, and an important topic is the study of slice knots and ribbon knots. A notorious open problem asks whether every slice knot is also ribbon.
Iterative algorithm. The definition of matrix multiplication is that if C = AB for an n × m matrix A and an m × p matrix B, then C is an n × p matrix with entries. From this, a simple algorithm can be constructed which loops over the indices i from 1 through n and j from 1 through p, computing the above using a nested loop: Input: matrices A ...
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