The phrase "increases to infinity" is correct and usable in written English.
It can be used in mathematical or theoretical contexts to describe a quantity that grows without bound.
Example: "As the value of x approaches zero, the function f(x) increases to infinity."
Alternatives: "grows indefinitely" or "tends towards infinity."
This stochastic differential equation has been introduced when studying the limit of systems of Brownian particles with electrostatic repulsion when the number of particles increases to infinity.
We show that in 1D and 2D the variance of the followers' deviation increases to infinity as one moves away from the leader, while in 3D the variance remains bounded regardless of the network size.
It is shown that under the protocol designed, all agents' states converge to a common Gaussian random variable, whose mathematical expectation is just the average of the initial states, and the mean square static error vanishes as the number of agents increases to infinity under certain topologies.
We show that accuracy of the method for quadratic functions improves with decreasing this parameter, however, at the same time, the condition number of the matrix M, which is the local matrix of the linear system for computing the discrete gradient, increases to infinity when the parameter goes to zero, so one needs to choose a compromise between accuracy and solvability of the local system.
This probability increases to 25.1 percent as the number of voters increases to infinity (keeping the number of candidates fixed) and to 100 percent as the number of candidates increases to infinity (keeping the number of voters fixed).
However, if the sample size (memory) increases to infinity, each of them are optimal.
Note that, while this straightforward learning algorithm was chosen for simplicity (i.e., resource preferences increase with increased feeding, but do not increase to infinity), complexity in the learning process arises in interaction with a diverse and spatial environment.
In all cases, a sudden increase to infinity of the relative electrical resistance corresponds to fiber fracture.
The entries have the form of smooth sequences that increase to infinity multiplied by proper periodic sequences.
Having read this I think I comprehend for the first time why it's always better to switch doors in the Monty Hall dilemma, and why the counting numbers increase to infinity but the supply of real numbers and transcendental numbers such as e and is infinitely larger than this infinity.
For instance, if ψ is any positive function increasing to infinity, there exists a symmetric central Gaussian semigroup having a continuous density such that log μt e)⩽log(1+1/t) ψ(1/t) as t tends to zero.
