If a sequence converges, then the value it converges to is unique. This value is called the limit of the sequence. The limit of a convergent sequence {\displaystyle (a_{n})} is normally denoted {\displaystyle \lim _{n\to \infty }a_{n}} . If {\displaystyle (a_{n})} is a divergent sequence, then the expression {\displaystyle \lim _{n\to \infty }a_{n}} is meaningless.
is defined as the set of all sequences {\displaystyle (x_{i})_{i\in \mathbb {N} }} such that for each i, {\displaystyle x_{i}} is an element of {\displaystyle X_{i}} . The canonical projections are the maps pi : X → Xi defined by the equation {\displaystyle p_{i}((x_{j})_{j\in \mathbb {N} })=x_{i}} . Then the product topology on X is defined to be the coarsest topology (i.e. the topology with the fewest open sets) for which all the projections pi are continuous. The product topology is sometimes called the Tychonoff topology.
LION also carries a heavy-duty, 6 wheel automatic numbering machine with rubber faced wheels. The rubber wheels work great for metal marking and plastic marking when used with LION fast dry ink. As with the other LION numbering machines, this machine is made in Japan with precision crafted one-piece hardened steel frame with all metal interior construction. LION machines will provide years of reliable use. Ideal for sequential numbering operations to use as a date and number stamp, serial number stamp, an inspection stamp and etc. sequential numbering in publisher